   Chapter 11, Problem 19RE ### 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

# In Problems 15-20, find the indicated derivative.Find d y / d x  for  3 x 2 + 2 x 3 y 2 − y 5 = 7.

To determine

To calculate: The value of dydx for the equation 3x2+2x3y2y5=7.

Explanation

Given Information:

The provided equation is:

3x2+2x3y2y5=7

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 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:

3x2+2x3y2y5=7

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

ddx(3x2+2x3y2y5)=ddx(7)

Now, use the chain rule of derivatives:

ddx(3x2+2x3y2y5

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