What is the derivative of $ln(sec^2 (x))$ ?

Question

16761 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-10T20:13:48

The derivative is $2tanx$ .

We can rewrite using trigonometry and the logarithm laws:

$y= ln(1/cos^2x) = ln(1) - ln(cos^2x) = 0 - ln((cosx)^2) = -2ln(cosx)$

Therefore by the chain rule

$y' = -2(-sinx)/cosx = (2sinx)/cosx = 2tanx$

Hopefully this helps!

What is the derivative of ln(sec^2 (x))ln(sec^2 (x))?