Problem of the Week

Updated at Mar 17, 2014 10:11 AM

For this week we've brought you this calculus problem.

How can we solve for the derivative of ln⁡(cos⁡x)\ln{(\cos{x})}?

Here are the steps:



ddxln⁡(cos⁡x)\frac{d}{dx} \ln{(\cos{x})}

1
Use Chain Rule on ddxln⁡(cos⁡x)\frac{d}{dx} \ln{(\cos{x})}. Let u=cos⁡xu=\cos{x}. The derivative of ln⁡u\ln{u} is 1u\frac{1}{u}.
1cos⁡x(ddxcos⁡x)\frac{1}{\cos{x}}(\frac{d}{dx} \cos{x})

2
Use Trigonometric Differentiation: the derivative of cos⁡x\cos{x} is −sin⁡x-\sin{x}.
−sin⁡xcos⁡x-\frac{\sin{x}}{\cos{x}}

Done
Cymath foriOSAndroid