what is the deravetives of e^(square root of x)?

Question

please thank you

Answer 1

Chain Rule

y = e^sqrt x

y' = e^sqrt x * 1 / (2sqrt x) = (e^sqrt x) / (2sqrt x)

Answer 2

The derivative of e ^sqrt(x) is e^sqrt(x) multiplied by the derivative of the exponent which is:

.5x^-.5=1/2sqrt(x)

[e^sqrt(x)]/2sqrt(x) <==== answer

Answer 3

e^(x^(1/2))

use the chain rule:
let u = x^(1/2)
then d/du (u) = e^u

d/dx (x^(1/2)
1/2 * x^(-1/2)
1/[2x^(1/2)]


e^(x^(1/2)) * 1/[2x^(1/2)]

simplify
e^(x^(1/2)) / [ 2x^(1/2) ] <== answer

Answer 4

y = e^(sqrt(x))
Let u = sqrt(x)
Then y = e^u
dy/dx = dy/du * du/dx = e^u * 1/(2sqrt(x)
dy/dx = e^sqrrt(x)/(2sqrt(x))

Answer 5

e^sqrt(x) / 2sqrt(x)