Question

if y =(x*sin^-1x)/(√(1-x^2)) prove that
(1-x^2)dy/dx=x+(y/x)

Answer 1

first multiply both sides by √(1-x^2)

for x sin^-1 x
you'll need product rule, know what that is ?

Answer 2

yeah i know how to do but not getting the answer nah -_-
i used division ru;e
need help in
differenatition of xsin^-1x

Answer 3

x*1/(1-x^2)*-2x + sin^-1x ???????/

Answer 4

x*1/√(1-x^2)*-2x + sin^-1x

Answer 5

ok, diff. of sin^(-1) x is 1/ (sqrt (1-x^2)) right ?
[x sin^(-1)x ]' = x /(sqrt (1-x^2)) + sin^(-1) x
only

Answer 6

why the -2x ?

Answer 7

chain rule

Answer 8

someone told me to do that

Answer 9

oh, but if the function was something like sqrt (1-x^2), the you would get -2x
but the function here is just sin^-1 x
whose derivative is just 1/ (sqrt (1-x^2))

Answer 10

oh but still i m not getting teh answer -_-

Answer 11

i tried so many times

Answer 12

no question of chain rule because there's no composite function...
show your work, i'll spot the error

Answer 13

okay brb in 1 min

Answer 14

by that time, i'll post my way of doing it, not using quotient rule...

Answer 15

y =(x*sin^-1x)/(√(1-x^2))

y √(1-x^2) = x sin^-1 x
now differentiating w.r.t x

(dy/dx) (√(1-x^2) + y ([-2x]/[2(√(1-x^2)]) = x /(sqrt (1-x^2)) + sin^(-1) x
2 product rules .....

now from the question, y =(x*sin^-1x)/(√(1-x^2))
isolating sin^-1 x, we get
sin^-1 x = y √(1-x^2) / x

plugging this in,
(dy/dx) (√(1-x^2) + y ([-2x]/[2(√(1-x^2)]) = x /(sqrt (1-x^2)) +y √(1-x^2) / x

now multiplying both sides by √(1-x^2) , we get

(1-x^2)(dy/dx) -xy = x +y(1-x^2)/x
--->(1-x^2)(dy/dx) = x +y/x -xy+xy
(1-x^2)(dy/dx) = x+y/x
thats it!