   Chapter 11, Problem 15RE ### 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. I f   y   I n   x   =   5 y 2 +   11 ,  find  d y / d x .

To determine

To calculate: The value of dydx for the provided equation ylnx=5y2+11.

Explanation

Given Information:

The provided equation is:

ylnx=5y2+11

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:

ylnx=5y2+11

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

ddx(ylnx)=ddx(5y2+11)

Now use the product rule of derivatives,

ddx(uv)=udvdx+vdudx

To obtain the derivative of ylnx

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