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