   Chapter 11.6, Problem 25E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 11-30, find the indicated derivative using implicit differentiation. [HINT: See Example 1.] e x y 2 = 1 + e y ; d y d x

To determine

To calculate: The value of dydx for the equation exy2=1+ey using the implicit differentiation.

Explanation

Given information:

The provided equation is exy2=1+ey.

Formula used:

Quotient rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f'(x)g(x)f(x)g'(x)[g(x)]2

Where, g(x)0

The derivative of e raised to a function is,

ddxeu=eududx

The derivative of e raised to x is,

ddxex=ex

The derivative of function f(x)=un using the chain rule is,

f(x)=ddx(un)=nun1dudx

Where, u is the function of x.

Calculation:

Consider the equation,

exy2=1+ey

Take ddx of both sides of the above equation,

ddx(exy2)=ddx(1+ey)ddx(exy2)=(ddx(1)+ddxey)

The derivative of e raised to a function is ddxeu=eududx.

Apply the above formula and the quotient rule for the derivative of (exy2),

ddxexy2exddx(y2)(y2)2=(0+eydydx)ddxexy2exddx(y2)y4=ey

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