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Suppose w is a function of r and s and r = x y + y z^2, s = sin y+ e^(x z). Use the information...

Question:

Suppose {eq}w {/eq} is a function of {eq}r {/eq} and {eq}s{/eq} and {eq}r = x y + y z^2, s = sin y+ e^{(x z)}.{/eq} Use the information given below to compute {eq}w_y (-1,0,0) : w_r (0,1) = 2 , w_s (0,1) = 5. {/eq}

Using Chain Rule:

With the chain rule, the derivative of the compound functions can be calculated, that is, derivatives with respect to variables that the function does not directly depend on.

Answer and Explanation: 1

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Given the values and the variables: {eq}r = xy + y{z^2},s = siny + {e^{xz}},{w_r}\left( {0,1} \right) = 2,{w_s}\left( {0,1} \right) = 5 {/eq}, using...

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The Chain Rule for Partial Derivatives

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Chapter 14 / Lesson 4
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This lesson defines the chain rule. It goes on to explore the chain rule with partial derivatives and integrals of partial derivatives.


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