What is the derivative of ln(sec^2 (x))ln(sec2(x))?
1 Answer
Mar 10, 2018
The derivative is
Explanation:
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)y=ln(1cos2x)=ln(1)−ln(cos2x)=0−ln((cosx)2)=−2ln(cosx)
Therefore by the chain rule
y' = -2(-sinx)/cosx = (2sinx)/cosx = 2tanx
Hopefully this helps!
