Answered: In Exercises 11–28, calculate the…

In Exercises 11–28, calculate the derivative with respect to x of the other variable appearing in the equation. x4 + z4 = 1

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

In Exercises 11–28, calculate the derivative with respect to x of the other
variable appearing in the equation.

Expert Solution

Step 1

Given equation is

$x^{4} + z^{4} = 1$

Writing given equation in terms of x,

$z^{4} = 1 - x^{4} z = {(1 - x^{4})}^{\frac{1}{4}}$

Step 2

Let $u = 1 - x^{4}$

Differentiate u with respect to x,

$\frac{d u}{d x} = (0 - 4 x^{3}) d x \frac{d u}{d x} = - 4 x^{3}$

Step by step

Solved in 4 steps

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