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Calculating Derivative – A quotient of polynom and ln – Exercise 6333

Exercise

Find the derivative of the following function:

f(x)=\frac{x^2}{\ln x+1}

Final Answer


f'(x)=\frac{2x\ln x +x}{{(\ln x+1)}^2}

Solution

f(x)=\frac{x^2}{\ln x+1}

Using Derivative formulas and the quotient rule in Derivative Rules, we get the derivative:

f'(x)=\frac{2x(\ln x +1)-x^2\cdot\frac{1}{x}}{{(\ln x+1)}^2}=

One can simplify the derivative:

=\frac{2x\ln x +2x-x}{{(\ln x+1)}^2}=

=\frac{2x\ln x +x}{{(\ln x+1)}^2}

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