Derivative of e to the Power Csc Square Root x

We know the derivative of ex, which is ex.

(ex)' = ex

We can find the derivative of ecscx using chain rule.

Find ᵈʸ⁄d, if

y = ecscx

Let u = x.

y = ecscu

Let v = cscu.

y = ev

Now,

y = ev ----> y is a function of v

v = cscu ----> 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 = cscu and u = x.

Substitute v = cscu.

Substitute u = x.

Therefore,

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