# 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

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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...

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