Use the product rule to differentiate {eq}g(x) = (3x^3 + 2x)(4x^2 - 2) {/eq}
Question:
Use the product rule to differentiate {eq}g(x) = (3x^3 + 2x)(4x^2 - 2) {/eq}
Differentiation
Differentiation measures the sensitiveness of the change in the value of one variable with respect to another variable. The derivative is obtained after differentiating the equation.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerProduct rule of differentiation is used to differentiate when the product of two functions is given.
Suppose u and v are the two functions in...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:

from
Chapter 6 / Lesson 15Learn about product differentiation and how it is used in marketing. See product differentiation examples based on price, quality, location, and other factors.
Related to this Question
- Let G(x) = f(x)g(x) . (a) What is the product rule? Let F(x) = \frac{f(x)}{g(x)}. (b) Using the product rule, find the derivative of F(x) . (c) What is the name of this result? (d) Use this result to differentiate F(x) = \frac {(2x^4 + 3x^3)}{(x^{-
- Use the product rule to differentiate f(x) = (x^2 + 3x^2 )(x^{-1} + 4).
- Differentiate the following question by using constant rule, product rule, sum-difference rule, chain rule, or quotient rule. y = 2(7x^2 - x)^4
- Differentiate the following question by using constant rule, product rule, sum-difference rule, chain rule, or quotient rule. y = 12x^2 - 6x + 4
- Differentiate the following question by using constant rule, product rule, sum-difference rule, chain rule, or quotient rule. y = (1 + x^2)/(2 - x)
- Differentiate the following question by using constant rule, product rule, sum-difference rule, chain rule, or quotient rule. y = (5x + 1)(x + 4)
- Find the first derivative of the following. Do not use the product rule. Be sure to show intermediate work and do not simplify your answer. M = 30 - 5P^(-1) + 7P^3
- Find the first derivative of the following. The derivative can be found by using combinations of the constant rule, power function rule and sum-difference rule. Do not use the product rule. Be sure to show intermediate work and do not simplify your answer
- Find the first derivative of the following. Do not use the product rule. Be sure to show intermediate work and do not simplify your answer. F = (1/2)S^3(2S^2 - 3S - 6)
- Find the first derivative of the following. Do not use the product rule. Be sure to show intermediate work and do not simplify your answer. E = X^2(3X^2 - 6X^5)
- Find the derivative of the following function: f(x) = 3 \: ln(x).
- Find the derivative of the following function: y = 8.
- (a) Find a formula for h'(x) when h(x) = f(''g(x)). (b) Find \frac{dy}{dt} when y = \ln\space t^c , where c is constant. (c) If f is differentiable at x, find an expression for the derivative of \sqrt{f(x)} (d) Find the first and second derivative of
- Find the first derivative of the following function: Y = 2X3 - 3X2 + 2X - 50
- Find the first derivative of the following function: Y = 5X4/5 + 3X3 - 2X3/2 - 10
- Find the first derivative of the following function. Y = 16 - 4X^(1/2) + 6X^(-1/2)
- Find the derivative of the following function: (a) Y=e^x Inx
- Find the first derivative of the function. D = 10 - 6S^2 + 3S^(4/3)
- (a) Find the derivative of the following function: y = \sqrt {x+ \sqrt {x + \sqrt x . (b) If R = S, S = 1 + BK, and K = Ate + B, where \alpha, \beta, \gamma, p, A, and B are constants, find an expression for \frac {dR}{dt}
- find the derivative of the following functions Y=45X-0.5X2 Y=X3-8X2+57X+2 TR=100Q+10Q2 TC=182+56Q
- Find the first derivative of the following. Do not use the product rule. Be sure to show intermediate work and do not simplify your answer. N = -5P^(-3) + 7P^3 - 9P^(-2)
- Find the first derivative of the following. R = 3T^(3/2) - 2T^(1/3) - 3T^(4/3)
- Write the first derivative of the following function: X = 5Y - 2Y^2 + 10Y^-3 - 3Y^1/3
- Find the 2nd derivative for the following function: y = 3(4x + x^2)^{0.5}.
- Differentiate this implicit function: y lnx = xe^y
- Find the first derivative of the function below. B = 3Q^3 (2Q - 3Q^2)
- Find the first derivative of the function. J = 2K^2 + 4K^3 - 3
- Differentiate: (a) f(x) = e^{x^5 + 8} (b) f(x) = \ln (\frac{(x^2 + 5)^5}{\sqrt{6 - x)
- Find the derivative of each implicit function, where dY/dX = F_X/F_Y, provided that F_Y is not equal to 0. (a) F(x,y) = x^2 + y^2 + (xy)^1/3 = 0 (b) F(x,y) = x^2y + y^2x + xy = 0
- Find the derivative of each implicit function, where dY/dX = -F_X/F_Y, provided that F_Y does not equal 0. a) F(x,y) = x^2 + y^2 + (xy)^{1/3) = 0 }] b) F(x,y) = x^2 y + y^2 x + xy = 0
- 2. From the definition of the derivative (definition 5.3), find the derivative for each of the following functions: (a) f(x)=6x (b) f(x)=12x-2 (c) f(x) = kx2 for k a constant
- Find the following derivatives. A. f(x) = (3x^2 - 4)^5 B. f(x) = 4x^3 - 3x^2 + 2x ^{- 3} C. f(x) = \frac{x^2}{3} - \frac{3}{x^2}
- Find the total derivative dz/dy, given z = f(x, y) = 5x + xy - y^2, where x = g(y) = 3y^2.
- Find the derivatives for each function F(x)=(5x-3x^2)^3 F(x)=(x+1)/x^2 F(x,y)=4x^2-16xy+4y^2
- Find the first derivative of the following. Be sure to show intermediate work and do not simplify your answer. V = -2Q^(-1/2) + 3Q^2 - 2Q^(2/3)
- Find the first derivative of the function below. V = Q^2 - 2Q + 3Q^3
- Find the first derivative for the inverse of each of the following functions: a. Q = -3P + 652 b. P = 280 - 2/3Q
- Use implicit differentiation to find y' where x^4 + xy + 2y^2 = 4. Evaluate this at (1,1).
- Find the first derivative of the following. Be sure to show intermediate work and do not simplify your answer. Z = -6X^5 + 3X^3 - 2X
- Find the first derivative of the function: T = -2R^(-1) + 7R^(-3) - 48 + R^2.
- Write the first derivative of the following function: W = 10X + 3X^3 - 10X^2/3 + 5X^-2
- Find the first and second order derivatives of the following (a) y = 6x^2 +x^-4 (b) y = -5 ln(6.3).
- Find the first derivative of the following function. Q = 25 - 3S^2 + 5S^(-3)
- Find the first derivative of the function: Z = 20P^(1/4) (30P^(2/5)).
- a) Find the first and second derivatives of y = b^t (with b > 1). (b) Find the first and second derivative of y=x^5 e^x
- What is the value of the derivative dC/d(Y-T)? Y=C(Y-T)+ I(Y) + G C= 500+.75(Y-T) I = 50 + .1Y G = 300 T = 200
- Use logarithmic differentiation to find y' if y =\frac{(80x+3)^2}{(6x - 4)}.
- Find the partial derivative. f(x, y, z) = ln ( x^(0.5) y^(0.5) )
- Find the first and second order derivatives of the following: (a) y = 6x^2 + x^-4 (b) y= -5 ln(6x).
- Use derivatives to determine whether the following function is concave or convex. u = - 4 ln (6).
- Find all the first-order and second-order partial derivatives for the following function: z = (x+y)/(x-y)
- Use implicit differentiation to find y prime where x^4 + xy + 2y^2 = 4. Evaluate this at (1, 1).
- Use implicit differentiation to find y' where x^2 +6xy + 4y^3 = 20. Evaluate this at (x, y) = (2,1).
- Calculate the derivatives of the following functions: 1) y = 3x^{2} 2) y = \frac {5}{x^{2 3) y = 3x^{2} + 4x + 7
- Find the first order differential of the following functions: A. y = 3x^2 B. y = x^3 + 3x + 4x^2 + x C. y = (x + 1)^3 D. y = -3x - 3 E. y = (2x^4 + 9)^6 F. y = 2x^4 + 3x^2 + x^3 + c
- Use derivatives to determine whether the following function is concave or convex. u = 4e^-v/2
- Derive the Slutsky equation using calculus.
- Consider the function g(X) = 3X + 2. Find the expectation and variance of this function.
- Use implicit differentiation to find y' and y" where 2x^{2} + 6xy+ y^2=18. Evaluate these at (x, y) = (1,2).
- Consider the following multivariate function: Y = 6X_1 X_2^(1/2) i) Find the partial derivative of Y with respect to X_1 ii) Find the partial derivative of Y with respect to X_2
- (a) Let f(x) be a function having a second-order derivative f"(x). What is the condition for finding an inflection point of f(x)? (b) Suppose f(1) = 4x^3 - 2x^2. Find any inflection points f(x) may have.
- (a) Let f(x) be a function having a second-order derivative f"(x). What is the condition for finding an inflection point of f(x)? (b) Suppose f(x) = 4x^3 -2x^2. Find any inflection points f(x) may have.
- Find the slope of the function f(x) = x^{1/2}, x \geq 0.
- Let f and g be two strictly concave functions and let function h be defined by = af + bg, where a is greater than 0 and b is greater than 0 are constants. Using the definition of strict concavity (
- Consider the multivariate function below: Y = -20 + 113.75 X1 + 80 X2 - 10 X21 - 10 X2 i) Find the partial derivative of Y with respect to X1 ii) Find the partial derivative of Y with respect to X2
- Find and interpret the partial derivatives for the Cobb-Douglas production function with two inputs:
- Find the values of x_1, and x_2 at which the functions: (a) f(x_1, x_2) = (x_1 - 2)^2 + (x_2 - 1 )^2, and (b) f(x_1, x_2) = (x_1 - 2)^2 - (x_2 ? 1)^2 have both partial derivatives equal to zero, but s
- 1) Find the first derivative of the following function in the space provided Y = 13 + 3X - 2X^2 + 3X^3 2) Find the first derivative of the following function in the space provided S = 10W + 4W^2 - 10W^{ - 3} + 3W^{1/ 3}
- Let f(x) = 3x + 2x^3. A) Define the "Newton quotient" for this function at the point x = a. B) Simplify this by canceling "h" from the numerator and the denominator, where possible. C) Find the limit of the "Newton quotient" for "h" approaching zero. D) B
- If J = 2K^3 + 4K^2 - 3, find first derivative of dJ/dK.
- Find and interpret the second-order partial derivatives of the Cobb-Douglas production function with two inputs.
- Let. a. Define the "Newton quotient" for this function at the point. b. Simplify this by canceling "h" from the numerator and the denominator, where possible. c. Find the limit of the "Newton quotient" for "h" approaching zero. d. By definition, what is t
- U(x_1,x_2)= 10(x_1)^2(x_2)^3, what is the answer differentiation x_1 and differentiation x_2?
- Suppose that f(x) is a concave function and g(x) is a function that is both increasing and concave. See if you can show that the composite function y(x) = f(g(x)) is also concave.
- If f(x)=\frac{x^2}{\ln(x)}. Find f'x.
- Find h'(x) for the following function: h(x) = frac{1 + x}{x - 2}. Draw a graph of h(x).
- U=alnx+Blny. Show that the first derivative of the Marshallian demand for x with respect to px can be obtained through the Slutsky decomposition. Make sure to identify the income and the substitution
- Consider a function y = f(x). (a) What is the definition of the differential of y with respect to x (b) Let y = 4x +2 ln(x+e). Find \Delta Y (the actual change in y) and dy (the differential) at x=0 if dx = 0.01.
- Are the following functions monotonic transformations? You can determine it by drawing a graph or calculating their derivatives. Assume u \ge 0 throughout. (a) f(u) = ln(u+1) (b) f(u) = u^3 (c) f(u) = u^2/(u + 1)
- For the function x2 + y2 = 81, find the slope of the tangent to the curve at x = -1.5.
- For the function y x 2 3 x 3 x , a t 2 , 0 find the following: a The slope of the tangent line find the following a the slope of the tangent line b The instantaneous rate of change of the function
- To calculate the slope of the total product curve: a) take the change in y divided by the change in x b) find the slope of a line tangent to the TP curve c) subtract the change in y from the change in x d) subtract the change in x from the change in y
- To maximize or minimize a function Y in terms of an independent variable X, the rule is Select one: a. find Y where dX/dY=0 b. find X where dY/dX is maximized or minimized. c. find XX where dY/dX=0
- Find the deriviate of the following fuctions y=45X-0.5X^2 y=X^3-8X^2+57X+2 TR=100Q-10Q^2 TC=182+56Q
- Derive the IS curve. In your answer outline the properties of the IS curve. And explain using graphs as well.
- Find the ?rst and second derivative of each function and determine whether each function is convex or concave. If it is both, ?nd the ranges for which it is convex and ranges for which it is concave:
- Derive an expression for the asymptotic variance of the TSLS estimator.
- Consider the function y = -2.05 + 1.06x - 0.04x^2. Find all the critical points of y and use the first and second derivative tests to classify them.
- Show that Cobb-Douglas function with decreasing returns to scale is strictly concave using hessian of second derivatives and the definition of the concavity.
- Verify if the following indefinite integral is correct \int (18(3x + 2)(1+x)e^{6x} + \frac{4}{x}) dx = (3x + 2)^2e^{6x} + 4 \ln |x|+C.
- Verify if the following indefinite integral is correct \int (18(3x + 2)(1+x)e^{6x} + \frac{4}{x}) dx = (3x + 2)^2e^{6x} +4 In \left | x \right | +C.