   Chapter 11.3, Problem 21E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find d y / d x for x 4 + 3 x 3 y 2 − 2 y 5 = ( 2 x + 3 y ) 2

To determine

To calculate: The value of dydx for the provided equation x4+3x3y22y5=(2x+3y)2.

Explanation

Given Information:

The provided equation is, x4+3x3y22y5=(2x+3y)2.

Formula used:

When y is an implied function of x, obtain dydx by differentiating both sides of the equation with respect to x and then algebraically solve for dydx.

According to the product rule of derivatives,

ddx(uv)=udvdx+vdudx

According to the chain rule, if f and g are differentiable functions with y=f(u) and u=g(x), then y is a differentiable function of x and:

dydx=dydududx

Calculation:

Consider the provided equation,

x4+3x3y22y5=(2x+3y)2

First, take the derivative of both sides of the equation with respect to x as,

ddx(x4+3x3y22y5)=ddy(2x+3y)2

Now use the product rule of derivatives,

ddx(uv)=udvdx+vdudx

To obtain the derivative of x3y2

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