Question

How do you find the derivative of `f(x)=e^(sqrtx)`?

Answer 1

`d/dx (e^sqrtx) = e^sqrtx/(2sqrtx)`

Explanation:

Using the chain rule:

`d/dx f(y(x)) = (df)/dy xx dy/dx`

with `y=sqrtx`:

`d/dx (e^sqrtx) = (d/dy e^y) (d/dx sqrt x)`

`d/dx (e^sqrtx) = e^y/(2sqrtx)`

`d/dx (e^sqrtx) = e^sqrtx/(2sqrtx)`