Home
Class 12
MATHS
If y = sin (log (e) x) then (x ^(2) (d ^...

If `y = sin (log _(e) x)` then `(x ^(2) (d ^(2) y)/(dx ^(2)) +x (dy )/(dx)=`

A

`sin(log_(e)x)`

B

`cos(log_(e)x)`

C

`y^(2)`

D

`-y`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    SIA PUBLICATION|Exercise Problems|48 Videos

  • EAMCET - 2018 (TS) SHIFT - 1

    SIA PUBLICATION|Exercise EXERCISE - Chemistry|8 Videos

Similar Questions

Explore conceptually related problems

x = cos theta, y = sin 5 theta implies (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))-x(dy)/(dx)0 .

Cos^(-1) ((y)/(b)) =2 log "" ((x)/(2)) , x gt 0 implies x ^(2) (a ^(2) y)/(dx ^(2)) + x (dy )/(dx) =

If y = (lot _(e) x)/(x) and z = log _(e) x, then (d ^(2) y)/(dz^(2)) + (dy)/(dz) =

If y= sin x +e^(x) then (d^2x)/(dy^2) =

If y=e ^(-2x) sin ^(3) x , then (d^(2)y)/dx^(2) =

If x+ y = sin(x+y) then (dy)/(dx) =

If y = log _(cos x ) sin x, then , (dy)/(dx ) =

Show that (d ^(2)x)/( dy^2) =- ((d ^(2) y )/( dx ^(2))) ((dy)/(dx)) ^(-3)

SIA PUBLICATION-DIFFERENTIATION -Problems
  1. y=e^(asin^(-1x))rArr(1-x^(2))y(n+2)-(2n+1)xy(n+1) is equal to

    Text Solution

    |

  2. If x = a{costheta + log tan((theta)/(2))} andy = a sin theta, then (dy...

    Text Solution

    |

  3. If y = sin (log (e) x) then (x ^(2) (d ^(2) y)/(dx ^(2)) +x (dy )/(dx)...

    Text Solution

    |

  4. If 2x^(2) - 3xy + y^(2) + x + 2y - 8 = 0, then (dy)/(dx) is equal to

    Text Solution

    |

  5. If y = log {((1 +x)/(1-x )) ^(1//4) } -1/2 Tan ^(-1) (x ), then (dy)/(...

    Text Solution

    |

  6. x = cos theta, y = sin 5 theta implies (1- x ^(2)) (d^(2)y)/(dx ^(2)) ...

    Text Solution

    |

  7. x ^(y) =y ^(x) implies x ( x-y log x ) (dy)/(dx) =

    Text Solution

    |

  8. If f(x) = e^(x) sin x, then f^((6)) (x) is equal to

    Text Solution

    |

  9. IF f : R to R is an even function which is twice differentiable on R a...

    Text Solution

    |

  10. Statement I : f(x) = ax^(41) + bx^(-40) rArr (f'(x))/(f(x)) = 1640...

    Text Solution

    |

  11. f (x) = 10 cos x + (13 + 2x) sin x implies f''(x) + f(x) =

    Text Solution

    |

  12. x sqrt(1 + y) + y sqrt(1 + x) =0implies (dy)/(dx)=

    Text Solution

    |

  13. If x ^(y) = e ^(x -y) then (dy)/(dx) =

    Text Solution

    |

  14. y = Sin ^(-1) x implies ( 1- x ^(2)) (d ^(2) y)/(dx ^(2)) =

    Text Solution

    |

  15. If f(x) = (1)/(x^(2)) int(3)^(x)(2t-3f'(t)dt, then f'(3) is equal to

    Text Solution

    |

  16. If f (x) = e ^(x) , g (x) = Sin ^(-1) x and h (x) =f (g (x)), then (h'...

    Text Solution

    |

  17. If y = sqrt(ax) + (a ^(2))/(sqrt(ax))then y (1) , y (2) at x =a are

    Text Solution

    |

  18. If y = ae^(x) + be^(-x) + c, where a, b, c are parameters, then y'' is...

    Text Solution

    |

  19. If y =a cos (log x) + b sin (log x) then x ^(2) y (2) + xy (1)+y=

    Text Solution

    |

  20. If h (x) = e ^(e ^(x)) then (h '(x))/( h(x))

    Text Solution

    |