Home
Class 12
MATHS
If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1...

If `y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)(dy)/(dx)` is equal to (a)`x+y` (b) `1+x y` (c)`1-x y` (d) `x y-2`

A

x+y

B

1+xy

C

1-xy

D

xy-2

Text Solution

Verified by Experts

`y=(sin^(-1))/(sqrt(1-x^(2)))`
`therefore" "(dy)/(dx)=(sqrt(1-x^(2))(1)/(sqrt(1-x^(2)))-(sin^(-1)x)(1)/(2)((-2x))/(sqrt(1-x^(2))))/(1-x^(2))`
`"or "(1-x^(2))(dy)/(dx)=1+x((sin^(-1)x)/(sqrt(1-x^(2))))=1+xy`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|23 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.9|14 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=sqrt((1-x)/(1+x))," then "(1-x^(2))(dy)/(dx) is equal to

If y=(sin^(-1) x)/(sqrt(1-x^2)) , then show that (1-x^2)(d^2y)/(dx^2)-3x(dy)/(dx)-y=0 .

If y=sin^(-1) x, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to (a) n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

If y=sqrt((1-x)/(1+x)) , prove that , (1-x^(2)) (dy)/(dx)+y=0

If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) is equal to (a) 1/(2(1+x^2)),x in R (b) 1/(2(1+x^2)),x >0 (c) (-1)/(2(1+x^2)),x<0 (d) 1/(2(1+x^2)),x<0

If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to (a) x/y (b) y/(x^2) (C) (x^2-y^2)/(x^2+y^2) (d) y/x

If y=(x+sqrt(1+x^(2)))^(n) , then (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to -

If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx) at x=0 is

If y=sqrt((1-x)/(1+x)) ,prove that (1-x^2)dy/dx+y=0

CENGAGE PUBLICATION-DIFFERENTIATION-Execrises
  1. If f(x) = x + tan x and f is the inverse of g, then g'(x) is equal to

    Text Solution

    |

  2. If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the val...

    Text Solution

    |

  3. If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)(dy)/(dx) is equal to (a)...

    Text Solution

    |

  4. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...

    Text Solution

    |

  5. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b...

    Text Solution

    |

  6. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  7. answeer the following : (i) if y sqrt(x^2+1)=log(sqrt(x^2+1)-x), show ...

    Text Solution

    |

  8. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

    Text Solution

    |

  9. or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...

    Text Solution

    |

  10. "If "log(e)((e-1)e^(xy)+x^(2))=x^(2)+y^(2),then (dy)/(dx) at (1, 0) is...

    Text Solution

    |

  11. If y=x^((x^(x))) then (dy)/(dx) is

    Text Solution

    |

  12. The first derivative of the function [cos^(-1)(s insqrt((1+x)/2))+x^x]...

    Text Solution

    |

  13. Let f(x)=x^(x),x in (0,oo) and let g(x) be inverse of f(x), then g'(x)...

    Text Solution

    |

  14. If y=a x^(n)+b x^(-n),then x^2(d^2y)/(dx^2) is equal to

    Text Solution

    |

  15. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to (a) n(n-1)...

    Text Solution

    |

  16. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f^(prime prime)(x...

    Text Solution

    |

  17. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto 2^(20)(cos2x-2^(20)os3x...

    Text Solution

    |

  18. (d^n)/(dx^n)(logx)=? (a)((n-1)!)/(x^n) (b) (n !)/(x^n) (c)((n-2)!)/(...

    Text Solution

    |

  19. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

    Text Solution

    |

  20. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

    Text Solution

    |