Question

find dy/dx of y = squrt ln x?

Answer 1

dy/dx = 1/(2x(sqrt ln x))
To solve, make the equation:
y^2 = ln x
And differentiate.

Answer 2

To see this, let \[u=\ln x \]Then, the chain rule says\[dy/dx=(dy/du)(du/dx)\]We have:\[dy/du=1/(2\sqrt{u})\]And,\[du/dx=1/x\]So,\[dy/dx=(dy/du)(du/dx)=(1/(2\sqrt{u})(1/x)\]Replacing u= lnx our final answer is\[dy/dx=1/(2x \sqrt{lnx})\]