   Chapter 11.6, Problem 26E 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.] x e y + x y = 9 y ; d y d x

To determine

To calculate: The value of dydx for the equation xey+xy=9y using the implicit differentiation.

Explanation

Given information:

The provided equation is xey+xy=9y.

Formula used:

Product 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).

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.

Constant multiple rule of derivative of function f(x) is f'(cx)=cf'(x) where c is constant.

Calculation:

Consider the equation,

xey+xy=9y

Take ddx of both sides of the above equation,

ddx(xey+xy)=ddx(9y)ddx(xey)+ddx(xy)=ddx(9y)

Apply the product rule for the derivative of (xy) and the quotient rule for the derivative of (xey),

(dxdxeyxddxey(ey)2)+(dxdxy+xdydx)=ddx(9y)(1eyxddxeye2y)+(1y+xdydx)=ddx(9y)(eyxddxeye2y)+(y+xdydx)=ddx(9y)

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

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