# 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(cos(x)*e^x+e^x*sin(x))/cos(x)^2