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 excos⁡x\frac{{e}^{x}}{\cos{x}}?

Check out the solution below!



ddxexcos⁡x\frac{d}{dx} \frac{{e}^{x}}{\cos{x}}

1
Use Quotient Rule to find the derivative of excos⁡x\frac{{e}^{x}}{\cos{x}}. The quotient rule states that (fg)′=f′g−fg′g2(\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}.
cos⁡x(ddxex)−ex(ddxcos⁡x)cos⁡2x\frac{\cos{x}(\frac{d}{dx} {e}^{x})-{e}^{x}(\frac{d}{dx} \cos{x})}{\cos^{2}x}

2
The derivative of ex{e}^{x} is ex{e}^{x}.
cos⁡xex−ex(ddxcos⁡x)cos⁡2x\frac{\cos{x}{e}^{x}-{e}^{x}(\frac{d}{dx} \cos{x})}{\cos^{2}x}

3
Use Trigonometric Differentiation: the derivative of cos⁡x\cos{x} is −sin⁡x-\sin{x}.
cos⁡xex+exsin⁡xcos⁡2x\frac{\cos{x}{e}^{x}+{e}^{x}\sin{x}}{\cos^{2}x}

Done
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