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what is derivative of secx^2

Guest Oct 9, 2014

Best Answer 

 #2
avatar+94105 
+10

$$\frac{d}{dx}sec^2x\\\\
=\frac{d}{dx}(cosx)^{-2}\\\\
=-2(cosx)^{-3}(-sinx)\\\\
=-2(cosx)^{-3}(-sinx)\\\\
=2(cosx)^{-3}(sinx)\\\\
=\frac{2sinx}{(cosx)^{3}}\\\\
or\\\\
=2tanx\;sec^2x$$

 or

 

$$\\2tanx(tan^2x+1)\\\\
or\\\\
2tan^3x+2tanx$$

 

I got a different answer from Chris - I haven't checked it

Melody  Oct 9, 2014
 #1
avatar+92673 
+5

d/dx(secx)2 = (using the chain rule)

2(secx)(tanx)2

----------------------------------------------------------------------------------------------------------------

Edit..........

Whoops...... I made a slight error......

The derivative of the sec x = sec xtanx...so the final result should be, as Melody said,

2(secx)(secxtanx) = 2tanx(secx)^2

Thanks, Melody, for catching my error !!!!!!

 

CPhill  Oct 9, 2014
 #2
avatar+94105 
+10
Best Answer

$$\frac{d}{dx}sec^2x\\\\
=\frac{d}{dx}(cosx)^{-2}\\\\
=-2(cosx)^{-3}(-sinx)\\\\
=-2(cosx)^{-3}(-sinx)\\\\
=2(cosx)^{-3}(sinx)\\\\
=\frac{2sinx}{(cosx)^{3}}\\\\
or\\\\
=2tanx\;sec^2x$$

 or

 

$$\\2tanx(tan^2x+1)\\\\
or\\\\
2tan^3x+2tanx$$

 

I got a different answer from Chris - I haven't checked it

Melody  Oct 9, 2014
 #3
avatar+94105 
0

It wasn't much of an error Chris, you didn't need to take your points away! I'll give them back to you.   :)

Melody  Oct 9, 2014
 #4
avatar+92673 
0

Nope....I'm "zapping" myself for that stupid error......I should have checked my work more closely !!!!

 

 

CPhill  Oct 9, 2014
 #5
avatar+94105 
0

You can't take away my points to you.  It is not polite to throw a gift in the bin!

Melody  Oct 9, 2014
 #6
avatar
0

You are a surgeon with numbers; just sharpen your machete :)

Guest Oct 9, 2014
 #7
avatar+94105 
0

Me or Chris?

Melody  Oct 9, 2014
 #8
avatar+92673 
0

My "machete" made a hash of that one !!!!

 

CPhill  Oct 9, 2014
 #9
avatar+92673 
0

Your "machete" is sharp enough, Melody.......mine needs to go back for a little more honing.......

 

CPhill  Oct 9, 2014
 #10
avatar+94105 
0

Yea - I don't have a machete 

My tools are much more refined   LOL

Melody  Oct 9, 2014
 #11
avatar
0

You are not the first surgeon to k**l a patient. Remember they get to bury their mistakes;  mathematicians get to erace theirs. This is the lament: remembering to use a pencel and not a pen.

Guest Oct 9, 2014

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