Question

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

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

Answer 1

another product rule problem

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

actually \(x\) is a variable, \(e^x\) is a function, although it too varies according to \(x\)

Answer 6

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

Answer 7

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