Home
Class 12
MATHS
If x=f(t) and y=g(t), then (d^2y)/(dx^2)...

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

Text Solution

Verified by Experts

Given,`x=f(t),y=g(t)`
`(dx)/(dt)​=f′(t) `
`(dy)/(dt)​=g′(t)`
`(dy)/(dx)​=((dx)/(dt)/(​dy)/(dt))​​=(g′(t))/(f′(t))`
​ ...
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 x=f(t) and y=g(t), then (d^(2)y)/(dx^(2)) is equal to

If x=f(t) and y=g(t), then (d^(2)y)/(dx^(2)) is equal to (f'g-g'backslash f)/((f')^(3))(b)(f'g-g'backslash f)/((f')^(2))(c)(g)/(f)(d)(f^(g)-gf')/((g')^(3))

If x = t^(2) and y = t^(3) , then (d^(2)y)/(dx^(2)) is equal to

If x = t^(2) and y = t^(3) , then (d^(2)y)/(dx^(2)) is equal to

If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to

If y =f (x) and z=g(x) then (d^(2)y)/(dx ^(2)) equals

If x=t^(2) and y=t^(3)+1 , then (d^(2)y)/(dx^(2)) is

If x=at^(2),y=2at, then (d^(2)y)/(dx^(2)) is equal to ( a )-(1)/(t^(2))( b) (1)/(2at^(2))(c)-(1)/(t^(3)) (d) (1)/(2at^(3))

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If y=Acosn x+Bsinn x , show that (d^2y)/(dx^2)+n^2\ y=0 .

    Text Solution

    |

  14. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

    Text Solution

    |

  15. If y=Acos(logx)+\ Bsin(logx) , prove that x^2\ (d^2y)/(dx^2)+x(dy)/(dx...

    Text Solution

    |

  16. If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

    Text Solution

    |

  17. If y=tanx , prove that y2=2y y1 .

    Text Solution

    |

  18. If y=tan^(-1)x , find (d^2y)/(dx^2) in terms of y alone.

    Text Solution

    |

  19. If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

    Text Solution

    |

  20. If y^3-y=2x , prove that (d^2y)/(dx^2)=-(24 y)/((3y^2-1)^3) .

    Text Solution

    |