   Chapter 11, Problem 18RE ### 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  x 2 + 3 y 2 + 2 x − 3 y + 2 = 0.

To determine

To calculate: The value of dydx for the provided equation x2+3y2+2x3y+2=0.

Explanation

Given Information:

The provided equation is:

x2+3y2+2x3y+2=0

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:

x2+3y2+2x3y+2=0

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

ddx(x2+3y2+2x3y+2)=ddx(0)

Now, use the chain rule of derivatives:

dydx=dydududx

To obtain the derivatives of y

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