If `y = e^(m sin^(-1) x) and (1-x^(2)) ((dy)/(dx))^(2) = Ay^(2)` , then A is equal to

Options

A. m
B. `-m`
C. `m^(2)`
D. `- m^(2)`

Answer

C

Explanation

Given , ` y = e^(m^(sin^(-1))) x ` …(i)
On differentiatig both sides w.r.t.w, we get
` (dy)/(dx) = e^(msin^(-1)x) (d)/(dx) (m sin ^(-1) x)`
` rArr (dy)/(dx) = e^(msin^(-1)x)(mxx(1)/(sqrt( 1 - x^(2))))`
`rArr sqrt( 1 - x^(2)) (dy)/(dx) = my " " [from Eq . (i) ] `
On squaring both sides , we get
`(1 - x^(2))((dy)/(dx))^(2) = m^(2) y^(2)`
But it is given , that `(1 - x^(2))((dy)/(dx))^(2) = Ay^(2)`
`therefore A = m^(2)` .