Derivative of inverse secant

  • Thread starter biochem850
  • Start date
  • #1
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Homework Statement



Find the derivative of sec[itex]^{-1}[/itex]([itex]\frac{\sqrt{1+x^{2}}}{x}[/itex])

Homework Equations



sec[itex]^{-1}[/itex]=[itex]\frac{U'}{U\sqrt{U^{2}-1}}[/itex]


The Attempt at a Solution



U'=-[itex]\frac{1}{x^{2}\sqrt{1+x^{2}}}[/itex]



U[itex]\sqrt{U^{2}-1}[/itex]= [itex]\frac{\sqrt{1+x^{2}}}{x^{2}}[/itex]


Therefore the derivative is -[itex]\frac{1}{1+x^{2}}[/itex]


I'm starring to feel more confident with these derivatives and if this is correct, I think I will have come ever closer to mastering this skill. Can someone tell me if this is correct (the answer isn't in my text)?

p.s. I know that the first "U" in the denominator of the relevant equation should be in absolute value brackets but I couldn't find them in the menu.

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Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
Your answer is right.
 
  • #3
51
0
Your answer is right.

Thank you
 

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