How do you differentiate #f(x)= 7xsin2x# using the product rule?

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Answer 1

Oct 24, 2016

#f'(x)=7sinx+14xcos2x#

The product rule of derivatives is:
#color(blue)((u(x)*v(x))'=u'(x)*v(x)+v'(x)*u(x))#

#f'(x)=7(xsin2x)'#

#f'(x)=7*(color(blue)(x'sinx+x(sin2x)'))#
#f'(x)=7*(1*sinx+x(2cos2x)#
#f'(x)=7*(sinx+2xcos2x)#
#f'(x)=7sinx+14xcos2x#