Find derivative of sec x cot x

We know that $\sec x = \frac{1}{\cos x}$ and $\cot x = \frac{\cos x}{\sin x}$.

$$f(x) = \frac{1}{\cos x} \cdot \frac{\cos x}{\sin x}$$ $$f(x) = \frac{1}{\sin x}$$ $$f(x) = \csc x$$

The derivative of $\csc x$ is $-\csc x \cot x$.

$$\frac{d}{dx}(\csc x) = -\csc x \cot x$$

Therefore, the derivative of $\sec x \cot x$ is: