Problem of the Week

Updated at Nov 3, 2014 12:49 PM

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

How would you differentiate \(\cos{x}-{e}^{x}\)?

Check out the solution below!



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

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} \cos{x})-(\frac{d}{dx} {e}^{x})\]

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

3
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[-\sin{x}-{e}^{x}\]

Done
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