Home
Class 12
MATHS
"if "y=sin^(-1)[sqrt(x)sqrt(1-x^(2))-x s...

`"if "y=sin^(-1)[sqrt(x)sqrt(1-x^(2))-x sqrt(1-x)]``and 0lt x lt 1," then find "(dy)/(dx).`

Text Solution

Verified by Experts

`y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]," where "0lt x lt 1`
`=sin^(-1)[xsqrt(1-(sqrt(x))^(2))-sqrt(x)sqrt(1-x^(2))]`
`=sin^(-1)x-sin^(-1)sqrt(x)`
`[because sin^(-1) x-sin^(-1)y=sin^(-1)(xsqrt(1-y^(2))-ysqrt(1-x^(2)))]`
Differentiating w.r.t.x, we get
`(dy)/(dx)=(1)/(sqrt(1-x^(2)))-(1)/(sqrt(1-(sqrt(x))^(2)))(d)/(dx)(sqrt(x))`
`=(1)/(sqrt(1-x^(2)))-(1)/(sqrt(1-x))xx(1)/(2sqrt(x))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Solved Examples|28 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If y=sin^(-1)(sqrt(1-x^2]) and 0 < x < 1, then find (dy)/(dx)

Find int(sin^(-1)x)/(sqrt(1-x^(2)))dx

y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)] then find dy/dx

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , (0 lt x lt pi/2) , then (dy)/(dx)=

If ysqrt(1-x^2)+xsqrt(1-y^2)=1 when |x|lt1 and |y|lt1 find dy/dx

Find (dy)/(dx)," if "y= sin^(-1)x +sin^(-1)sqrt(1-x^(2)), 0 lt x lt 1 .

y= tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))) , where -1 < x < 1 , find dy/dx

If y = tan^(-1) ((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) show that (dy)/(dx) = x/sqrt(1-x^4) .

Solve x-sqrt(1-|x|) lt 0 .

If x sqrt(1-y^(2))+y sqrt(1-x^(2))=k , then the value of (dy)/(dx) at x=0 is -