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}

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! 

Share with Friends

Leave a Reply