# Problem of the Week

## Updated at Apr 27, 2015 9:06 AM

For this week we've brought you this calculus problem.

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

Here are the steps:

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

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