# Find the value of the second derivative at the given point.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.3, Problem 28E
To determine

## Find the value of the second derivative at the given point.

Expert Solution

The value of f"(π6)=14 .

### Explanation of Solution

Given:

The given function is f(t)=csct and the given pointis f"(π6) .

Calculation:

Find the second derivative of the function.

f(t)=csctf'(t)=csctcott

Apply product rule.

(fg)'=gf'+fg'

f"(t)=[cottddt(csct)+csctddt(cott)]

Use derivative rule ddx(cscx)=cosxcotx and ddx(cotx)=csc2x .

f"(t)=[cott(csctcotx)+csct(csc2t)]f"(t)=csctcot2t+csc3t

f"(π6)=csc(π6)cot2(π6)+csc3(π6)=2(3)2+23=6+8=14

Hence thevalueof f"(π6)=14 .

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