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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