Derivative of e to the Power Square Root Tanx

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

(e^x)' = e^x

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

Find ᵈʸ⁄dₓ, if

y = e^√tanx

Let u = tanx.

y = e^√u

Let v = √u.

y = e^v

Now,

y = e^v ----> y is a function of v

v = √u ----> v is is a function of u

u = tanx ----> u is is a function of x

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

Substitute y = e^v, v = √u and u = tanx.

Substitute v = √u.

Substitute u = tanx.

Therefore,

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