Problem of the Week

Updated at Mar 13, 2017 3:23 PM

This week we have another calculus problem:

How can we solve for the derivative of \(\frac{{x}^{5}}{\sin{x}}\)?

Let's start!



\[\frac{d}{dx} \frac{{x}^{5}}{\sin{x}}\]

1
Use Quotient Rule to find the derivative of \(\frac{{x}^{5}}{\sin{x}}\). The quotient rule states that \((\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}\).
\[\frac{\sin{x}(\frac{d}{dx} {x}^{5})-{x}^{5}(\frac{d}{dx} \sin{x})}{\sin^{2}x}\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\frac{5{x}^{4}\sin{x}-{x}^{5}(\frac{d}{dx} \sin{x})}{\sin^{2}x}\]

3
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[\frac{5{x}^{4}\sin{x}-{x}^{5}\cos{x}}{\sin^{2}x}\]

Done
Cymath foriOSAndroid