Question

What is the derivative of `f(x)=1/sinx`?

Answer 1

Since `f(x)=1/(sin(x))=csc(x)`, the answer can be written down from memorization that `f'(x)=-csc(x)cot(x)`.

Alternatively, the Quotient Rule can be used: `f'(x)=\frac{sin(x)*0-1*cos(x)}{sin^{2}(x)}=-\frac{cos(x)}{sin^{2}(x)}`

`=-\frac{1}{sin(x)}*\frac{cos(x)}{sin(x)}=-csc(x)cot(x)`