How do you differentiate #f(x)=(x-3lnx)(tanx+2x)# using the product rule?

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How do you differentiate #f(x)=(x-3lnx)(tanx+2x)# using the product rule?

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Answer 1 · 2015-12-31T08:24:58

The product rule #(uv)'=uv'+vu'# where #u# and #v# are functions of #x# Our answer would be #f'(x) = (x-3ln(x))(sec^2(x) + 2)+(tan(x)+2x)(1-3/x)#

Explanation:

To differentiate
#f(x) = (x-3ln(x))(tan(x)+2x)#
#f'(x) = (x-3ln(x))d/dx(tan(x)+2x) + (tan(x)+2x)d/dx(x-3ln(x))#
#f'(x) = (x-3ln(x)){d/dx(tan(x) + d/dx(2x)} + (tan(x)+2x){d/dx(x) - d/dx(3ln(x))}#

#f'(x) = (x-3ln(x))(sec^2(x) + 2)+(tan(x)+2x)(1-3/x)# Answer

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How do you differentiate #f(x)=(x-3lnx)(tanx+2x)# using the product rule?

1 Answer

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