How do you differentiate #f(x)=(x^2+sinx)(x-cosx)# using the product rule?

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How do you differentiate #f(x)=(x^2+sinx)(x-cosx)# using the product rule?

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Answer 1 · 2018-05-13T15:34:19

#=3x^2-xcosx+(1+x^2)sinx-cos2x#

Explanation:

#f(x)=(x^2+sinx)(x−cosx)#
#f^'(x)=(x^2+sinx)d/dx(x−cosx)+(x−cosx)d/dx(x^2+sinx)#
#=(x^2+sinx)(1+sinx)+(x−cosx)(2x+cosx)#
#=x^2+sinx+x^2sinx+sin^2x+2x^2-2xcosx+xcosx-cos^2x#
#=sin^2x-cos^2x+sinx(1+x^2)-xcosx+3x^2#
#=3x^2-xcosx+(1+x^2)sinx-cos2x#

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How do you differentiate #f(x)=(x^2+sinx)(x-cosx)# using the product rule?

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