Derivative of e to the Power Cot Square Root x

We know the derivative of ex, which is ex.

(ex)' = ex

We can find the derivative of etanx using chain rule.

Find ᵈʸ⁄d, if

y = ecotx

Let u = x.

y = ecotu


Let v = cotu.

y = ev

Now,

y = ev ----> y is a function of v

v = cotu ----> 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 = ev, v = cotu and u = x.

Substitute v = cotu.

Substitute u = x.

Therefore,

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