calculus derivatives

Question

g(x)=e^root x

Answer 1

g(x) = e^√x

g'(x) = e^√x (√x)' = e^√x [(1/2)x^-1/2] = e^√x / (2√x)

Answer 2

Given that the function is g(x)=e^√x.

To find the derivative of the function g'(x)

Use chain rule formula to find the derivative g'(x).

The chain rule formula is as follows.

g'(x)=f'(h(x)).h'(x)

Differentiate the function with respect to x as shown beolw.

g'(x)=d/dx(e^√x).d/dx(√x)

g'(x)=e^√x.d/dx(x^(1/2))

g'(x)=e^√x.1/2x^(1/2-1)

g'(x)=e^√x.1/2x^(-1/2)

g'(x)=e^√x/2√x

The derivative of the function g(x)=e^√x is e^√x/2√x.

Answer 3

g(x) = e^√∫x

^{g'(x) =} e^√∫x (1/2x^^-1/2) = e^√x / (2√x)