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Question: Which of the following is the derivative of f (x) = cosh- 1 (cosec 8x)?


A ) cosec 8x
B ) tan 8x
C ) sec 8x
D ) 16cosec 16x
E ) - 8cosec 8x

Steps to derive

1 f (x) = cosh- 1 (cosec 8x)
 [Write the function.]

2 f  ′(x) = ddx [cosh- 1 (cosec 8x)]
 [Find f  ′(x).]

3 = 1cosec2 8x-1 (- 8cosec 8x cot 8x)
 [Use Chain Rule.]

4 = 1cot 8x (- 8cosec 8x cot 8x)

5 = - 8cosec 8x
 [Simplify.]

6 The derivative of cosh- 1 (cosec 8x) is - 8cosec 8x



Hence the right answer is Option E

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