Question

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

Answer 1

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

Explanation:

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`