Exercise
Find the derivative of the following function:
f(x)=\frac{1}{x}\ln x^2
Final Answer
Solution
We arrange the function before differentiating:
f(x)=\frac{1}{x}\ln x^2=
=\frac{\ln x^2}{x}
Using Derivative formulas and the quotient rule in Derivative Rules, we get the derivative:
f'(x)=\frac{\frac{1}{x^2}\cdot 2x\cdot x-\ln x^2\cdot 1}{x^2}=
One can simplify the derivative:
=\frac{2-\ln x^2}{x^2}
Note: You can also leave the function as a multiplication of two functions and derive it using the multiplication rule in derivation rules. It leads to the same result, of course.
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