We know the derivative of e^{x}, which is e^{x}.
(e^{x})' = e^{x}
We can find the derivative of e^{ln(√x)} using chain rule.
Find ᵈʸ⁄dₓ, if
y = e^{ln(√x)}
Let u = √x.
y = e^{ln(}^{u)}
Let v = ln(u).
y = e^{v}
Now,
y = e^{v} ----> 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 = e^{v}, v = cotu and u = √x.
Substitute v = ln(u).
Substitute u = √x.
Therefore,
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