We know the derivative of ex, which is ex.
(ex)' = ex
We can find the derivative of elnx using chain rule.
If y = elnx, find ᵈʸ⁄dₓ.
y = elnx
Let t = lnx.
Then, we have
y = et
Now, y = et 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 = et and t = 2x.
Substitute t = lnx.
Use the identity, elnx = x.
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