   Chapter 11.6, Problem 2E 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.] 4 x − 5 x = 9

To determine

To calculate: The value of dydx for the equation 4x5y=9 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 4x5y=9.

Formula used:

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

f'(cx)=cf'(x)

Where, c is constant.

Calculation:

Consider the equation, 4x5y=9

Take ddx of both sides,

ddx(4x5y)=ddx(9)ddx(4x)ddx(5y)=ddx(9)

Apply constant multiple rule for the derivative of (4x) and (5y),

4dxdx5dydx=0415dydx=045dydx=0

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

5dydx=04=4

Simplify the derivative through dividing both sides by (5),

55dydx=45dydx=45

Thus, the value of dydx for equation 4x5y=9 is 45 using the implicit differentiation

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