Find {eq}f'(x) {/eq} if {eq}f(x) = x^3 (x^2 + 3)^3 {/eq}
Question:
Find {eq}f'(x) {/eq} if {eq}f(x) = x^3 (x^2 + 3)^3 {/eq}
Product Rule of Derivative:
The given function {eq}f(x) {/eq} represents a multiplication of two functions. If we speculated these two functions are {eq}g(x) \, and \, h(x) {/eq} then we can write:
{eq}g(x) = x^3 \, or \, (x^2 +3)^3 {/eq}
And:
{eq}h(x) = x^3 \, or \, (x^2 +3)^3 {/eq}
Now:
We are imploring to locate {eq}f'(x) {/eq} and we realize that {eq}f'(x) {/eq} is computed by the Product Rule of Derivative.
The Rule is clarified below:
Product Rule of Derivative:
{eq}\frac{d}{dx} (f(x)g(x)) = f(x) \frac{d}{dx} (g(x)) + g(x) \frac{d}{dx} (f(x)) {/eq}
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerThe function is given by:
{eq}f(x) = x^3 (x^2 + 3)^3 {/eq}
Derivative of {eq}f(x) {/eq} with respect to {eq}x {/eq} is:
{eq}\begin{align*} f^...
See full answer below.
Learn more about this topic:
from
Chapter 7 / Lesson 5The derivative in calculus is the rate of change of a function. In this lesson, explore this definition in greater depth and learn how to write derivatives.