Problem of the Week

Updated at Dec 28, 2015 3:43 PM

This week we have another calculus problem:

How would you differentiate \(\frac{5x}{{e}^{x}}\)?

Let's start!



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

1
Use Constant Factor Rule: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\).
\[5(\frac{d}{dx} \frac{x}{{e}^{x}})\]

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[5\times \frac{{e}^{x}-x(\frac{d}{dx} {e}^{x})}{{e}^{2x}}\]

4
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[\frac{5({e}^{x}-x{e}^{x})}{{e}^{2x}}\]

Done
Cymath foriOSAndroid