Question

dy/dx arcsin(1/x) my answer was

-1 / x^2 sqrt(1 - 1/x^2) wolfram says this is correct, but my book shows answer as

-1 / (x sqrt(x^2 - 1))

Im struggling to see how they are equivalent.

Answer 1

i think it is just a matter of subtracting

Answer 2

\[1-\frac{1}{x^2}\]
\[\frac{x^2-1}{x^2}\]

Answer 3

math books abhor complex fractions. it is clear now right?

Answer 4

the
\[x^2\] comes out of the square root as an x and cancels with one of them

Answer 5

I think so, algebra is killing me here I think. Yes, that makes it clear
thank you

Answer 6

your last bit about what happens with x helped most. Thank you. I hate complex fractions. :(

Answer 7

i can write it out if you like

Answer 8

No, I see it now sqrt 1/x^2 is just 1/x x^2/x = x. got it.

Answer 9

\[\frac{-1}{ x^2 \sqrt{1 - \frac{1}{x^2}}} \]
\[\frac{-1}{x^2\sqrt{\frac{x^2-1}{x^2}}}\]
\[\frac{-1}{\frac{x^2}{x}\sqrt{x^2-1}}\]

Answer 10

thank you.

Answer 11

yw