Question

How do you find the derivative of `e^(1/x)`?

Answer 1

`(-e^(1/x))/x^2`

Explanation:

Since the derivative of `e^x` is just `e^x`, application of the chain rule to a composite function with `e^x` as the outside function means that:

`d/dx(e^f(x))=e^f(x)*f'(x)`

So, since the power of `e` is `1/x`, we will multiply `e^(1/x)` by the derivative of `1/x`.

Since `1/x=x^-1`, its derivative is `-x^-2=-1/x^2`.

Thus,

`d/dx(e^(1/x))=e^(1/x)*(-1/x^2)=(-e^(1/x))/x^2`