Derivative of e to the Power Square Root Cosx

We know the derivative of ex, which is ex.

(ex)' = ex

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

Find ᵈʸ⁄d, if

y = e√cosx

Let u = cosx.

y = e√u

Let v = √u.

y = ev

Now,

y = ev ----> y is a function of v

v = √u ----> v is is a function of u

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

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

Substitute y = ev, v = √u and u = cosx.

Substitute v = √u.

Substitute u = cosx.

Therefore,

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