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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.