   Chapter 9.5, Problem 14E ### 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 11-20, find the indicated derivatives and simplify. d s d t  for  s = t 3 − 4 t 3 − 2 t 2 − t − 5

To determine

To calculate: The derivative of the expression (t34)(t32t2t5) with simplification.

Explanation

Given Information:

The provided expression is (t34)(t32t2t5).

Formula Used:

The quotient rule:

If two functions are given in the form f(x)g(x), then the derivative is given as,

ddx(fg)=f.gg.fg2

Calculation:

Consider the provided expression is (t34)(t32t2t5).

In the expression, the value of,

f(t)=(t34)

And

g(t)=(t32t2t5)

Apply the quotient rule of the expression,

ddt(fg)=ddt(t34).(t32t2t5)ddt(t32t2t5).(t34)(t32t2t5)2

Evaluate the expression further,

ddt(fg)=(ddt(t3)ddt(4)).(t32t2t5)(ddt(t3)2ddt(t2)ddt(t)ddt(5))

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