Derivative of e to the Power ln(x)

We know the derivative of ex, which is ex.

(ex)' = ex

We can find the derivative of eln(x) using chain rule.

Find ᵈʸ⁄d, if

y = eln(x)

Let u = x.

y = eln(u)

Let v = ln(u).

y = ev


y = ev ----> y is a function of v

v = ln(u) ----> 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 = ln(u).

Substitute u = x.


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