# Problem of the Week:Derivative of $$\ln{x}\sin{x}$$

Updated at Jan 23, 2017 1:26 PM

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

How would you solve for the derivative of $$\ln{x}\sin{x}$$?

Here're the steps:

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

 1 Use the 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 The derivative of $$\sin{x}$$ is $$\cos{x}$$$\frac{\sin{x}}{x}+\ln{x}\cos{x}$Donesin(x)/x+ln(x)*cos(x)