# Chapter 14 - Partial Derivatives - Review - Concept Check - Page 1021: 11

See the explanation below.

#### Work Step by Step

The chain rule states that when a function $z=f(x,y)$ is differentiable function of $x$ and $y$ where $x=g(s),y=h(s)$ are function of a single variable let us say $s$, that is, $x,y$ are both differnatible functions of $s$.Then $\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x}\dfrac{dx}{dt}+\dfrac{\partial f}{\partial y}\dfrac{dy}{dt}$ Also, the chain rule states that when a function $z=f(x,y)$ is differentiable function of $x$ and $y$ where $x=g(s),y=h(s)$ are function of two variables let us say $s,t$, that is, $x,y$ are both differnatible functions of $s,t$.Then $\dfrac{\partial z}{\partial s}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial s}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial s}$ and $\dfrac{\partial z}{\partial t}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial t}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial t}$

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