Problem of the Week

Updated at May 19, 2014 11:07 AM

How would you differentiate \(\frac{5}{8\cos{x}}\)?

Below is the solution.



\[\frac{d}{dx} \frac{5}{8\cos{x}}\]

1
Use Constant Factor Rule: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\).
\[\frac{5}{8}(\frac{d}{dx} \frac{1}{\cos{x}})\]

2
Use Chain Rule on \(\frac{d}{dx} \frac{1}{\cos{x}}\). Let \(u=\cos{x}\). Use Power Rule: \(\frac{d}{du} {u}^{n}=n{u}^{n-1}\).
\[\frac{5}{8}\times \frac{-1}{\cos^{2}x}(\frac{d}{dx} \cos{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[\frac{5\sin{x}}{8\cos^{2}x}\]

Done
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