Derivative of e to the Power Lnx

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

(e^x)' = e^x

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

If y = e^lnx, find ᵈʸ⁄dₓ.

y = e^lnx

Let t = lnx.

Then, we have

y = e^t

Now, y = e^t and t = lnx. That is, y is a function of t and t is a function of x.  

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

Substitute y = e^t and t = 2x.

Substitute t = lnx.

Use the identity, e^lnx = x.

Therefore,

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