We know the derivative of ln(x), which is ¹⁄ₓ.
[ln(x)]' = ¹⁄ₓ
We can find the derivative of ln(√x) using chain rule.
Find ᵈʸ⁄dₓ, if
y = ln(√x)
Let u = √x.
y = ln(u)
y = ln(u) ----> y 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 = ln(u) and u = √x.
Substitute u = √x.
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