How do you differentiate #f(x)=(1-x)tan^2(2x)# using the product rule?

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Answer 1 · 2016-01-11T12:52:07

Step by step working shown below.

#f(x)=(1-x)tan^2(2x)#

This problem would require product rule and chain rule.

The product rule.

#(uv)'=uv'+vu'#

#f'(x) = (1-x)d/dx(tan^2(2x))+tan^2(2x)d/dx(1-x)#

For derivating #tan^2(2x)# we need to use the chain rule.

#f'(x) = (1-x){2tan(2x)d/dx(tan(2x))} + tan^2(2x)(-1)#

#f'(x)=(1-x){2tan(2x)sec^2(2x)d/dx(2x)} - tan^2(2x)#

#f'(x) = (1-x){2tan(2x)sec^2(2x)(2)}-tan^2(2x)#

#f'(x)=4(1-x)tan(2x)sec^2(2x)-tan^2(2x)#