Question

What is the derivative of `e^(1/x)`?

Answer 1

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

Explanation:

To find derivative of `e^(1/x)`, we use function of a function i.e. if `f(g(x))`, `(df)/(dx)=(df)/(dg)xx(dg)/(dx)`

Hence `d/(dx)e^(1/x)` is equal to

`e^(1/x)xxd/(dx)(1/x)=e^(1/x)xx(-1/x^2)=-e^(1/x)/x^2`