Copyright

Suppose f is a differentiable function of x and y , and g ( r , s ) = f ( 4 r ? s , s 2 ? 5...

Question:

Suppose {eq}f {/eq} is a differentiable function of {eq}x {/eq} and {eq}y {/eq}, and {eq}g(r, s) = f(4r - s, s^2 - 5r) {/eq}. Use the table of values below to calculate {eq}g_r(3, 5) {/eq} and {eq}g_s(3, 5) {/eq}.

{eq}\begin{array}{c|c|c|c|c} & f & g & f_x & f_y \\ \hline (7,10) & 2 & 6 & 9 & 3 \\ \hline (3,5) & 6 & 2 & 8 & 7 \end{array} {/eq}

Partial Derivatives:

In a multivariable case, partial derivatives only differentiate the variables specified by the partial derivative operator. This means that variables not specified are treated as constant values.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

Given: {eq}g(r, s) = f(4r-s,s^2-5r) \\ \begin{array}{c|c|c|c|c} & f & g & f_x & f_y \\ \hline (7,10) & 2 & 6 & 9 & 3 \\ \hline (3,5) & 6 & 2 & 8...

See full answer below.


Learn more about this topic:

Loading...
Partial Derivative: Definition, Rules & Examples

from

Chapter 18 / Lesson 12
24K

What is a Partial Derivative? Learn to define first and second order partial derivatives. Learn the rules and formula for partial derivatives. See examples.


Related to this Question

Explore our homework questions and answers library