Question

How do you differentiate `f(x)= (xe^x+x)^2` using the chain rule.?

Answer 1

`f^'(x)=2x(e^x+1)(xe^x+e^x+1)`

Explanation:

`f(x)=(xe^x+x)^2`
`=>f^'(x)=2(xe^x+x)^(2-1)*d/(dx)(xe^x+x)`
`=>f^'(x)=2(xe^x+x)[xd/(dx)(e^x)+e^xd/(dx)(x)+1]`
`=2(xe^x+x)(xe^x+e^x+1)`
`f^'(x)=2x(e^x+1)(xe^x+e^x+1)`