If `y = e^(m) sin^(-1) x and (1-x^(2)) ((dy)/(dx))^(2) = At^(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 differentiating both sides w.r.t.x. we get
`(dy)/(dx)=e^(m^(sin(-1))) (d)/(dx)(m sin^(-1)x)`
`Rightarrow (dy)/(dx)=e^(m^(sin^(-1))) (mxx(1)/(sqrt(1-x^(2))))`
`Rightarrow 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 `(t-x^(2)) ((dy)/(dx))^(2)=Ay^2`
`A=m^(2)`