Use the chain rule to find expressions for partial z by partial u and partial z by partial w if z...


Use the chain rule to find expressions for {eq}\frac{\partial z}{\partial u}{/eq} and {eq}\frac{\partial z}{\partial w}{/eq} if

{eq}z=f(x,y), \quad x=h(u,w), \quad y=g(w,t){/eq}

(Just in case, there are no typos in the above formulas. In particular, {eq}x{/eq} does not depend on {eq}t{/eq} and {eq}y{/eq} does not depend on {eq}u.{/eq})

Chain Rule:

The chain rule is a mathematical operation that is used in differential calculus to differentiate composite functions. Chain rule to be applicable, the composition of the composite function should be differentiable.

Answer and Explanation: 1

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Given data

  • The given function are;

{eq}z = f\left( {x,y} \right)............\left( 1 \right) {/eq}

{eq}x = h\left( {u,w} \right)............\left(...

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Learn more about this topic:

The Chain Rule for Partial Derivatives


Chapter 14 / Lesson 4

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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