Differentiate the function: f(x) = (x^(3) +2x)e^(x).

Please show how, I want to learn how to do it, rather than just get the answer.

Question

Differentiate the function: f(x) = (x^(3) +2x)e^(x).

Please show how, I want to learn how to do it, rather than just get the answer.

anonymous · Answer

$$f(x)=(x^3+2x)e^x$$ requires the product rule, because this is a multiplication

anonymous · Answer

use 
$$(fg)'=f'g+g'f$$ with $f(x)=x^3+2x,f'(x)=3x^2+2,g(x)=e^x,g'(x)=e^x$

anonymous · Answer

so you would get something like:
(x^(3)+2x)e^(x) + e^(x)(3x^(2) + 2) ?

anonymous · Answer

The derivative of e^(x) is itself right?

anonymous · Answer

of course in order to use the product rule you have to know the derivative of each factor, other wise you cannot use it. 
i hope it is clear that the derivative of $x^3+2x$ is $3x^2+2$ by the power rule, and also that the derivative of $e^x$ is $e^x$

anonymous · Answer

yes. and yes your above answer is correct, although you can now do some algebra to clean it up a little

anonymous · Answer

okay :)
So taking the derivatives of e^(of something) is new to me. How would you do xe^(-kx)?

anonymous · Answer

I will ask this in a different question, so I can award you a medal again.

anonymous · Answer

I'm going to close this question, and start a new one. It will be up to you to help me ^^, but I'm not good with taking the derivatives of 'e'