Home
Class 12
MATHS
If y=sin^(-1)x ,s howt h a t(d^2y)/(dx^...

If `y=sin^(-1)x ,s howt h a t(d^2y)/(dx^2)=x/((1-x^2)^(3/2))`

Text Solution

Verified by Experts

`y=(sin^(−1)x)^2 `
on differentiating wrt x we get
`⇒(dy)/(dx)​=2sin^(−1)x×1/(sqrt(1−x^2)) ​ _______ (1)`
again differentiating wrt x we get
`⇒(d^2y)/(dx^2)​=2[1/(sqrt(1−x2))xxsqrt(1-x^2)]/(1-x^2)-sin^(-1)(1x-2x)/(2sqrt(1-x^2))`
...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If y=sin^(-1)x, show that (d^(2)y)/(dx^(2))=(1)/((1-x^(2))^(3/2))

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

If y=sin^(-1)x , show that (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0 .

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

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

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

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

If y=sin(2sin^-1x) show that (1-x^2)(d^2y)/(dx^2)= xdy/dx-4y

If e^(y)(x+1)=1, show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2) If y=sin(2sin^(-1)x), show that ((1-x^(2))d^(2y))/(dx^(2))=x(dy)/(dx)-4y

Q.if log y=sin^(-1)x, show that,(1-x^(2))((d^(2)y)/(dx^(2)))=x((dy)/(dx))+y

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y^3-y=2x ,p rov et h a t(d^2y)/(dx^2)=(-24 y)/((3y^2-1)^3)

    Text Solution

    |

  2. If y=x^x ,fin d(d^2y)/(dx^2)

    Text Solution

    |

  3. If y=sin^(-1)x ,s howt h a t(d^2y)/(dx^2)=x/((1-x^2)^(3/2))

    Text Solution

    |

  4. If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0

    Text Solution

    |

  5. If y=tanx+secx ,p rov et h a t(d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

    Text Solution

    |

  6. If y=(a x+b)/(x^2+c), then (2x y1+y) y3=

    Text Solution

    |

  7. If y=(log)e(x/a)^x ,then x^3y2=

    Text Solution

    |

  8. If sin^(-1) (1 – x) – 2sin^(-1) x = π / 2,then x is equal to

    Text Solution

    |

  9. If y=2/(sqrt(a^2-b^2)){tan^(-1)((a-b)/(a+b))tanx/2} , then show that (...

    Text Solution

    |

  10. If y=x^(n-1)lnx then x^2y2+(3-2n)x y1 is equal to -(n-1)^2y (b) (n...

    Text Solution

    |

  11. If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...

    Text Solution

    |

  12. If x=f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h ...

    Text Solution

    |

  13. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

    Text Solution

    |

  14. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

    Text Solution

    |

  15. If y=tan^-1((log(e/x^2))/(log(ex^2)))+tan^-1((3+2logx)/(1-6logx)), the...

    Text Solution

    |

  16. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)fx-xy(x)= 1 (b) -1...

    Text Solution

    |

  17. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosn x+isinn x)...

    Text Solution

    |

  18. (d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...

    Text Solution

    |

  19. If x=acosn t-bsinn t ,t h e n(d^2x)/(dt^2) is n^2x (b) -n^2x (c) -n ...

    Text Solution

    |

  20. In (dy)/(dx),x is a independent variable and y is the dependent vari...

    Text Solution

    |