What is the Derivative of Inverse Secant?

[biochem850]

Homework Statement

Find the derivative of sec$^{-1}$($\frac{\sqrt{1+x^{2}}}{x}$)

Homework Equations

sec$^{-1}$=$\frac{U'}{U\sqrt{U^{2}-1}}$

The Attempt at a Solution

U'=-$\frac{1}{x^{2}\sqrt{1+x^{2}}}$



U$\sqrt{U^{2}-1}$= $\frac{\sqrt{1+x^{2}}}{x^{2}}$


Therefore the derivative is -$\frac{1}{1+x^{2}}$


I'm staring 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.

 

[Dick]

Your answer is right.

 

[biochem850]

Your answer is right.

Thank you