Problem of the Week

Updated at Aug 19, 2013 3:54 PM

To get more practice in calculus, we brought you this problem of the week:

How can we find the derivative of \(\frac{{e}^{x}}{\cos{x}}\)?

Check out the solution below!



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

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

2
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[\frac{\cos{x}{e}^{x}-{e}^{x}(\frac{d}{dx} \cos{x})}{\cos^{2}x}\]

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

Done
Cymath foriOSAndroid