Problem of the Week

Updated at Feb 16, 2015 3:42 PM

How can we find the derivative of $${x}^{9}\ln{x}$$?

Below is the solution.

$\frac{d}{dx} {x}^{9}\ln{x}$

 1 Use Product Rule to find the derivative of $${x}^{9}\ln{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} {x}^{9})\ln{x}+{x}^{9}(\frac{d}{dx} \ln{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$9{x}^{8}\ln{x}+{x}^{9}(\frac{d}{dx} \ln{x})$3 The derivative of $$\ln{x}$$ is $$\frac{1}{x}$$.$9{x}^{8}\ln{x}+{x}^{8}$Done9*x^8*ln(x)+x^8