How do you differentiate #f(x)=(x+3)(x-1)cotx# using the product rule?

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Answer 1 · 2017-02-11T17:03:34

#f'(x)=(2x+2)cotx-(x^2+2x-3)csc^2x#

#f(x)=cotx(x+3)(x-1)=cotx(x^2+2x-3)#

#d/dxuv=vu'+uv'#

#u=cotx rarr(du)/dx=-csc^2x#
#v=x^2+2x-3 rarr(dv)/dx=2x+2#

#f'(x)=(2x+2)cotx-(x^2+2x-3)csc^2x#

How do you differentiate #f(x)=(x+3)*(x-1)*cotx# using the product rule?