Chapter 9.6, Problem 34E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 33 and 34, find the derivative of each function.(a) y = 3 ( 5 x ) 5 (b) y = 3 x 5 5 (c) y = 3 5 x 5 (d) y = ( 3 x ) 5 5

(a)

To determine

To calculate: The derivative of the function y=3(5x)5.

Explanation

Given Information:

The provided function is y=3(5x)5.

Formula used:

The power rule of differentiation,

ddxxn=nxnâˆ’1

Calculation:

Consider the provided function,

y=3(5x)5

Rewrite the function using 1an=aâˆ’n,

y=3(5x)âˆ’5

To find dydx differentiate both sides with respect to x,

dydx=ddx(3

(b)

To determine

To calculate: The derivative of the function y=3x55.

(c)

To determine

To calculate: The derivative of the function y=35x5.

(d)

To determine

To calculate: The derivative of the function y=(3x)55.

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