# How do you differentiate #f(x)=(sinx+lnx)(x-3e^x)# using the product rule?

##### 1 Answer

Jan 19, 2016

#### Answer:

#### Explanation:

The product rule states that if

#f'(x)=g'(x)h(x)+g(x)h'(x)#

In this instance, we have

#g(x)=sinx+lnxcolor(white)(xxxx)=>color(white)(xxxx)g'(x)=cosx+1/x#

#h(x)=x-3e^xcolor(white)(xxxx)=>color(white)(xxxx)h'(x)=1-3e^x#

Thus, we have

#f'(x)=(cosx+1/x)(x-3e^x)+(sinx+lnx)(1-3e^x)#