# Problem of the Week

## Updated at May 2, 2016 2:17 PM

How can we solve for the derivative of $$\cot{x}-\ln{x}$$?

Below is the solution.

$\frac{d}{dx} \cot{x}-\ln{x}$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dx} \cot{x})-(\frac{d}{dx} \ln{x})$2 Use Trigonometric Differentiation: the derivative of $$\cot{x}$$ is $$-\csc^{2}x$$.$-\csc^{2}x-(\frac{d}{dx} \ln{x})$3 The derivative of $$\ln{x}$$ is $$\frac{1}{x}$$.$-\csc^{2}x-\frac{1}{x}$Done-csc(x)^2-1/x