# Problem of the Week

## Updated at Aug 12, 2019 12:32 PM

How can we solve for the derivative of $$\csc{q}+{q}^{7}$$?

Below is the solution.

$\frac{d}{dq} \csc{q}+{q}^{7}$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dq} \csc{q})+(\frac{d}{dq} {q}^{7})$2 Use Trigonometric Differentiation: the derivative of $$\csc{x}$$ is $$-\csc{x}\cot{x}$$.$-\csc{q}\cot{q}+(\frac{d}{dq} {q}^{7})$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$-\csc{q}\cot{q}+7{q}^{6}$Done-csc(q)*cot(q)+7*q^6