# Problem of the Week

## Updated at Nov 18, 2013 1:12 PM

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

Below is the solution.

$\frac{d}{dx} \ln{x}\tan{x}$

 1 Use Product Rule to find the derivative of $$\ln{x}\tan{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} \ln{x})\tan{x}+\ln{x}(\frac{d}{dx} \tan{x})$2 The derivative of $$\ln{x}$$ is $$\frac{1}{x}$$.$\frac{\tan{x}}{x}+\ln{x}(\frac{d}{dx} \tan{x})$3 Use Trigonometric Differentiation: the derivative of $$\tan{x}$$ is $$\sec^{2}x$$.$\frac{\tan{x}}{x}+\ln{x}\sec^{2}x$Donetan(x)/x+ln(x)*sec(x)^2