Problem of the Week

Updated at May 19, 2014 11:07 AM

How would you differentiate 58cos⁡x\frac{5}{8\cos{x}}?

Below is the solution.



ddx58cos⁡x\frac{d}{dx} \frac{5}{8\cos{x}}

1
Use Constant Factor Rule: ddxcf(x)=c(ddxf(x))\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x)).
58(ddx1cos⁡x)\frac{5}{8}(\frac{d}{dx} \frac{1}{\cos{x}})

2
Use Chain Rule on ddx1cos⁡x\frac{d}{dx} \frac{1}{\cos{x}}. Let u=cos⁡xu=\cos{x}. Use Power Rule: dduun=nun−1\frac{d}{du} {u}^{n}=n{u}^{n-1}.
58×−1cos⁡2x(ddxcos⁡x)\frac{5}{8}\times \frac{-1}{\cos^{2}x}(\frac{d}{dx} \cos{x})

3
Use Trigonometric Differentiation: the derivative of cos⁡x\cos{x} is −sin⁡x-\sin{x}.
5sin⁡x8cos⁡2x\frac{5\sin{x}}{8\cos^{2}x}

Done
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