   Chapter 11.6, Problem 3E 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.] x 2 − 2 y = 6

To determine

To calculate: The value of dydx for the equation x22y=6 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 x22y=6.

Formula used:

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

f'(cx)=cf'(x)

Where, c is constant.

Calculation:

Consider the equation, x22y=6

Take ddx of both sides,

ddx(x22y)=ddx(6)ddx(x2)ddx(2y)=ddx(6)

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

2x2dydx=0

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

2dydx=02x=2x

Simplify the derivative through dividing both sides by (2),

22dydx=2x2dydx=x

Thus, the value of dydx for equation x22y=6 is x using the implicit differentiation

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