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

##### 1 Answer

Dec 26, 2015

#### Answer:

Apply the product rule to find:

#d/(dx) f(x) = (cos x + 1)(x+e^x) + (sin x + x)(1 + e^x)#

#### Explanation:

The product rule tells us that:

#d/(dx) u(x)v(x) = u'(x)v(x)+u(x)v'(x)#

So with

#d/(dx) f(x) = (cos x + 1)(x+e^x) + (sin x + x)(1 + e^x)#