What is y' when y=3xsinx?

In order to differentiate something like y=3xsinx, you need to make use of the product rule. The product rule says that when you have an equation in the form y=f(x)g(x), you can find y' by using the formula y'=f'(x)g(x) + g'(x)f(x).For the equation y=3xsinx, this basically means we can split it into two separate functions of x and differentiate them seperately. In this case we have, for example, that f(x)=3x and g(x)=sinx. So we have that f'(x)=3 and that g'(x)=cosx. By applying the product rule from above [y'=f'(x)g(x) + g'(x)f(x)], we have that y'=3sinx+3xcosx.This works for any y=f(x)g(x), as long as both f(x) and g(x) have valid derivatives.