Exercise
Find the derivative of the following function:
f(x)=\ln^2\sqrt{x}
Final Answer
Solution
We simplify the function before differentiating:
f(x)=\ln^2\sqrt{x}=
=\ln^2 x^{\frac{1}{2}}=
={(\frac{1}{2}\ln x)}^2=
=\frac{1}{4}\ln^2 x
Using Derivative formulas and the chain rule in Derivative Rules, we get the derivative:
f'(x)=\frac{1}{4}\cdot 2\ln x\cdot\frac{1}{x}=
One can simplify the derivative:
=\frac{\ln x}{2x}
Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions!