Question

Y=xsin^-1x/sqrt(1-x^2) prove that (1-x^2)dy/dx...........

Answer 1

Hii i am girl

y = xsin^-1 x/sqrt (1 - x^2)

let x= sin@

differentiating with respect to @

dX/d@ = cos@

cos@ = sqrt (1- x^2)

sec@= 1/sqrt(1 - x^2)

tan@ = x/sqrt(1- x^2)

@ = sin^-1x

y = sin@ @/cos@

y = tan@@

diffrenciating with respect to @

(dy/dx) cos@= sec^2@@ + tan@

dy/dx = secx (1/1- x^2 + (x/sqrt1-x^2)

(1 - x^2)dy/dx = (xsqrt(1 - x^2)+ 1)/sqrt(1 -x^2)

(1 - x^2)dy/dx =x +1/sqrt(1 - x^2)

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hope it may helps you