   Chapter 2.6, Problem 38E

Chapter
Section
Textbook Problem

# Find y ″ by implicit differentiation. x 3 − y 3 = 7

To determine

Tofind:

y"

by implicit differentiation.

Explanation

1) Concept:

To find y”, first differentiate the given equation with respect to x. Then solve it for y’.

Again differentiate the equation of y’ with respect to x to get y”.

2) Formula:

i. Constant Multiple rule

ddx cfx=  cddxfx

ii. Sum or difference rule

ddxfx ±gx=ddx fx± ddxgx

iii. The power rule

ddxxn=n xn-1

iv. Quotient rule

ddxfg=gddxf-fddxgg2

3) Given:

x3-y3=7

4) Calculation:

x3-y3=7

Differentiate with respect to x

ddxx3-y3=7

By Sum or difference rule of differnetiation

ddxx3-ddxy3=ddx7

ddxx3-ddxy3=7ddx1

3x2-3y2dydx=0

-3y2dydx=-3x2

dydx=3x23y2

dydx=x2y2

Differentiate with respect to x

dd

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 63-68, use the graph of the function f to determine limxf(x) and limxf(x) 64.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 37-48, compute and simplify so that only positive exponents remain. 48.

Mathematical Applications for the Management, Life, and Social Sciences

#### For y = f (u) and u = g(x), dydx=dydududx.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 