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How do you differentiate #f(x)=(cos^2x^2)^(7/3)# using the chain rule?

1 Answer

Sep 12, 2016

#-28/3xcos^(11/3)(x^2)sin(x^2)#

Explanation:

#f(x) = (cos^2x^2)^(7/3)#

#=(cos^(14/3)x^2)#

#f'(x) = 14/3* cos^(11/3)x^2 * d/dx(cosx^2)# (Power rule and Chain rule)

#= 14/3* cos^(11/3)x^2 * (-sinx^2) * 2x# (Chain rule)

#=-28/3xcos^(11/3)(x^2)sin(x^2)#

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