# Problem of the Week

## Updated at May 23, 2016 12:02 PM

How can we solve for the derivative of $$\ln{x}\cos{x}$$?

Below is the solution.

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

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