Exercise
Find the derivative of the following function:
f(x)=\ln\sqrt{a^2-x^2}
a is a parameter.
Final Answer
Solution
f(x)=\ln\sqrt{a^2-x^2}
Using Derivative formulas and chain rule in Derivative Rules, we get the derivative:
f'(x)=\frac{1}{\sqrt{a^2-x^2}}\cdot\frac{1}{2\sqrt{a^2-x^2}}\cdot (-2x)=
One can simplify the derivative:
=\frac{1}{2(a^2-x^2)}\cdot (-2x)=
=\frac{x}{x^2-a^2}
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