Derivative of secx

1. Rewrite the function to be differentiated:

   $$\sec{\left(x \right)} = \frac{1}{\cos{\left(x \right)}}$$

2. Let $u = \cos{\left(x \right)}$.

3. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$

4. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(x \right)}$:

   1. The derivative of cosine is negative sine:

      $$\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$$

   The result of the chain rule is:

   $$\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}$$

The answer is: