Derivative of e to the Power ln(√x)

We know the derivative of e^x, which is e^x.

(e^x)' = e^x

We can find the derivative of e^ln(√x) using chain rule.

Find ᵈʸ⁄dₓ, if

y = e^ln(√x)

Let u = √x.

y = e^ln(u)

Let v = ln(u).

y = e^v

Now,

y = e^v ----> y is a function of v

v = ln(u) ----> v is is a function of u

u = √x ----> u is is a function of x

By chain rule, the derivative of y with respect to x :

Substitute y = e^v, v = cotu and u = √x.

Substitute v = ln(u).

Substitute u = √x.

Therefore,

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.