Home
Class 12
MATHS
If y=sin^(-1)x , then show that (1-x^2)\...

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

Text Solution

Verified by Experts

We have given
`y=sin^(-1)x`
Then proof that `(1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0`
As, `y=sin^(-1)x`
Differentiating w.r.t.x
`(dy)/(dx)=(d(sin^(-1)x))/(dx)`
`(dy)/(dx)=1/(sqrt(1-x^2))`
`(sqrt(1-x^2))((dy)/(dx))=1`
...
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 (1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0 .

If y=asin^(-1)x , then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

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

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

If y=cos^(-1)x , then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

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

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

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

If y=sin^(-1)x, prove 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

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y=xlog[x/((a+b x))] , then show that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y...

    Text Solution

    |

  2. If y=log{x+ sqrt( x^2+a^2 )} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy...

    Text Solution

    |

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

    Text Solution

    |

  4. If y=e^(m\ sin^(-1)x) , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2...

    Text Solution

    |

  5. If y={x+sqrt(x^2+1)}^m , show that (x^2+1)y2+x y1-m^2\ y=0

    Text Solution

    |

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

    Text Solution

    |

  7. If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .

    Text Solution

    |

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

    Text Solution

    |

  9. Find (d^2y)/(dx^2) , if x=a t^2,\ \ y=2a t .

    Text Solution

    |

  10. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

    Text Solution

    |

  11. If y=asint and x=a(cost+logtant/2) , find (d^2y)/(dx^2) .

    Text Solution

    |

  12. lf x=acostheta+bsintheta, y=asintheta-bcostheta then show that y^2(d^...

    Text Solution

    |

  13. If x=sint,y=sinpt, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2 y=...

    Text Solution

    |

  14. If x=sintheta , y=cosptheta , prove that (1-x^2)y2-x y1+p^2y=0 , where...

    Text Solution

    |

  15. If (x-a)^2+(y-b)^2=c^2, for some c >0, p rov et h a t([1+((dy)/(dx))^...

    Text Solution

    |

  16. If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...

    Text Solution

    |

  17. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

    Text Solution

    |

  18. In (dy)/(dx),\ x is independent variable and y is the dependent va...

    Text Solution

    |

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

    Text Solution

    |

  20. Find second order derivative of x^3+tanx

    Text Solution

    |