Derivative of e to the Power Sin Square Root x

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

(e^x)' = e^x

We can find the derivative of e^sin√x using chain rule.

Find ᵈʸ⁄dₓ, if

y = e^sin√x

Let u = √x.

y = e^sinu

Let v = sinu.

y = e^v

Now,

y = e^v ----> y is a function of v

v = sinu ----> 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 = sinu and u = √x.

Substitute v = sinu.

Substitute u = √x.

Therefore,

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