# What is the derivative of #f(x)=ln(secx)#?

We can use the chain rule here and substitute the inside of the ln function as u. So:

Putting this into our equation for the derivative of an ln function we get:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of ( f(x) = \ln(\sec(x)) ), you would apply the chain rule:

[ f'(x) = \frac{d}{dx}[\ln(\sec(x))] = \frac{1}{\sec(x)} \cdot \frac{d}{dx}[\sec(x)] ]

Now, differentiate ( \sec(x) ) with respect to ( x ):

[ \frac{d}{dx}[\sec(x)] = \sec(x) \tan(x) ]

Substitute this result back into the original expression:

[ f'(x) = \frac{1}{\sec(x)} \cdot \sec(x) \tan(x) = \tan(x) ]

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7