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 \(\cos{x}\)
\[\frac{\sin{x}}{x}+\ln{x}\cos{x}\]

Done