How would you take the derivative of: f(x) = xe^(-kx)?

Please explain how to take derivatives of the variable 'e'.

Question

How would you take the derivative of: f(x) = xe^(-kx)?

Please explain how to take derivatives of the variable 'e'.

anonymous · Answer

another product rule problem

anonymous · Answer

the derivative of $e^x$ is $e^x$ so by the chain rule the derivative of $e^{-kx}$ is $-ke^{-kx}$ 
then apply the product rule

anonymous · Answer

you must understand one thing that e is not a variable its a constant
e^x is a variable.............................

anonymous · Answer

as before it is 
$$(fg)'=f'g+g'f$$ with $$f(x)=x,f'(x)=1,g(x)=e^{-kx},g'(x)=-ke^{-kx}$$

anonymous · Answer

actually $x$ is a variable, $e^x$ is a function, although it too varies according to $x$

anonymous · Answer

So whenever you have something like:
e^(ax), you would use the chain rule etc?

anonymous · Answer

although e^x is a function but still it varies with x hence its a variable.......