Question

y=sin^-1(2x/1+x^2) differentite

Answer 1

The derivative of the arcsine function is as follows\[\frac {d}{dx} \left[ \sin^{-1} u \right] = \frac {u'}{\sqrt {1 - u^2}}\]
Use that to find the derivative :)

Answer 2

ther's a shortcut,
put x= tan t

Answer 3

ok i try

Answer 4

cant we do it directly by using inverse trinometri derivative

Answer 5

algebraically cumbersome,putting x=tan t will simplify this greatly.

Answer 6

Hmm, Hartnn, how would we do it with that substitution? Would it require implicit differentiation?

Answer 7

its sin^-1tan2tan^-1x what to do next

Answer 8

see, x=tan t
means 2x/(1+x^2)=sin 2t
so sin^-1 sin 2t=2t=y
so y is just 2 tan^-1 x
so that u can use standard formula for tan^-1 x
got it?

Answer 9

2x/(1+x^2)=sin 2t from whre it came

Answer 10

2tan t /(1+tan^2 t)=2 tan t/sec^2 t=2sin t cos^2t/cos t=2 sin t cos t=sin 2t .........got it?