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How do you differentiate #f(x)=(e^x+x)(cotx+x)# using the product rule?

1 Answer

Mar 5, 2016

# [(e^x +1) * (cot x + x)] + [ (e^x +x) * (1 - csc^2x)]#

Explanation:

#d/dx e^x = e^x#

#d/dx x = 1#

#d/dx cot x = -csc^2x#

#d/dx x = 1#

According to product rule,
#f'(x) = [d/dx e^x + d/dx x] * (cot x + x) + (e^x +x) * [d/dx cot x + d/dx x]#

#= [(e^x +1) * (cot x + x)] + [ (e^x +x) * (1 - csc^2x)]#

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