   Chapter 11.6, Problem 4E 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 1–10, find d y / d x , using implicit differentiation. In each case, compare your answer with the result obtained by first solving for y as a function of x and then taking the derivative. [HINT: See Example 1.] 3 y + x 2 = 5

To determine

To calculate: The value of dydx for the equation 3y+x2=5 using the implicit differentiation. Also compare the result obtained by rearranging the equation for y as a function of x and taking the derivative.

Explanation

Given information:

The provided equation is 3y+x2=5.

Formula used:

Constant multiple rule of derivative of function f(x) is

f'(cx)=cf'(x) where c is constant.

Calculation:

Consider the equation, 3y+x2=5

Take ddx of both sides,

ddx(3y+x2)=ddx(5)ddx(3y)+ddx(x2)=ddx(5)

Apply constant multiple rule for the derivative of (3y) and take the derivative of (x2) which is equal to (2x),

3dydx+2x=0

Evaluate the value of dydx by isolating it to the left side,

3dydx=02x=2x

Simplify the derivative through dividing both sides by 3,

33dydx=2x3dydx=2x3

Thus, the value of dydx for equation 3y+x2=5 is 2x3 using the implicit differentiation

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