First derivative of sec^2(x)+tan^2(x).
The answer is 4sec^2(x)tanx, but I'm not sure how. Could anyone give my a step my step?

Question

First derivative of sec^2(x)+tan^2(x).
The answer is 4sec^2(x)tanx, but I'm not sure how. Could anyone give my a step my step?

myininaya · Answer

one way: you could use Pythagorean identity 
then differentiate

myininaya · Answer

recall 1+tan^2(x)=sec^2(x)

cheska_p · Answer

Let me try and work that out. I'll let you know if I get it this time

cheska_p · Answer

@myininaya I did get the correct answer this time. Thank you! Just wondering, would there be another way to get that answer without using the pythagorean trig identity?

myininaya · Answer

Let's see what happens if we differentiate the initial thing you have there without applying any identities
$$2 \sec(x) \cdot \sec(x) \tan(x)+2\tan(x) \cdot \sec^2(x) \$$
we don't need any identities

dinamix · Answer

$$(\sec^2x)'=2\sec^2xtanx$$ 

$$\tan^2x=2\tan(x)\sec^2x $$ cuz (tan(x))'=sec^2(x)

myininaya · Answer

these are like terms

dinamix · Answer

this my method @myininaya @cheska_P

dinamix · Answer

$$=\tan(x)[2\sec^2x+2\sec^2x]$$

cheska_p · Answer

@dinamix I'm so happy you did that method. I was doing that way originally and not getting the answer, BUT I completely forgot the derivative of tanx gives you sec^2x. I kept writing secx and didn't understand why I wasn't getting the answer! Thank you!!

dinamix · Answer

@cheska_P  u are welcome