Question

How do you find the derivative of `y=3^sqrtx`?

Answer 1

`(dy)/(dx)=(3^(sqrtx)ln3)/(2sqrtx)`

Explanation:

A `y=3^(sqrtx)`

`lny=sqrtxln3`

and `1/y(dy)/(dx)=1/(2sqrtx)xxln3`

or `(dy)/(dx)=ln3/(2sqrtx)xxy=ln3/(2sqrtx)xx3^(sqrtx)=(3^(sqrtx)ln3)/(2sqrtx)`