How do you differentiate #f(x)=cotx(cscx)#?

1 Answer
Tazwar Sikder
Sep 21, 2016

#- csc^(3)(x) - csc(x) cot^(2)(x)#

Explanation:

We have: #f(x) = cot(x) csc(x)#

This function can be differentiated using the "product rule":

#=> f'(x) = (d) / (dx) (cot(x)) cdot csc(x) + (d) / (dx) (csc(x)) cdot cot(x)#

#=> f'(x) = - csc^(2)(x) cdot csc(x) + (- csc(x) cot(x)) cdot cot(x)#

#=> f'(x) = - csc^(3)(x) - csc(x) cot^(2)(x)#

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