Use the Chain Rule to find partial z / partial s and partial z / partial t. z = (x - y)^7, x =...


Use the Chain Rule to find {eq}\frac{\partial z}{\partial s} \ and \ \frac{\partial z}{\partial t.}\\ z = (x - y)^7,\\ x = (s^2)t,\\ y = s(t^2). {/eq}

Partial Derivative:

If f is the functions of x,y and z, then its partial derivative {eq}\frac{\partial z}{\partial x} {/eq} can be derived by treating y as a constant. Similarly {eq}\frac{\partial z}{\partial y} {/eq} can be derived by treating x as a constant.

Answer and Explanation: 1

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We have,

{eq}z = (x-y)^7\\ x = s^2t\\ y =st^2 {/eq}

On differentiating, we get

{eq}\displaystyle \frac{\partial z}{\partial x}= 7(x-y)^6;\...

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Derivatives: The Formal Definition


Chapter 7 / Lesson 5

The derivative in calculus is the rate of change of a function. In this lesson, explore this definition in greater depth and learn how to write derivatives.

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