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

If `y=sin(log_(e)x)`, then `x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)` is equal to

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

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA|Exercise Exercise|60 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    OBJECTIVE RD SHARMA|Exercise Exercise|17 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

If y=cos(log x) , then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y is equal to

If y=cos (log x) ,then " "x^(2) (d^(2)y)/(dx^(2))+x(dy)/(dx)=

If y=sin((log)_e x) , then x^2\ (d^2y)/(dx^2)+x(dy)/(dx) is equal to.......

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

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

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

If y=sin(log x), then prove that (x^(2)d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0

If y =3 cos (log x) + 4 sin (log x), then x ^(2) (d ^(2) y )/( dx ^(2)) + x (dy)/(dx) =

If y=log (log 2x) ,then x ( d^(2)y)/(dx^(2))+(dy)/(dx) =

OBJECTIVE RD SHARMA-DIFFERENTIATION-Chapter Test
  1. If f(x)=sin{(pi)/(2)[x]-x^(5)},1ltxlt2 and [.] denotes the greatest in...

    Text Solution

    |

  2. If f(x) is a polynomial of degree n(gt2) and f(x)=f(alpha-x), (where ...

    Text Solution

    |

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

    Text Solution

    |

  4. If f(x)=(1-x)^(n), then the value of f(0)+f'(0)+(f''(0))/(2!)+...+(f...

    Text Solution

    |

  5. xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=

    Text Solution

    |

  6. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

    Text Solution

    |

  7. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

    Text Solution

    |

  8. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

    Text Solution

    |

  9. y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)]

    Text Solution

    |

  10. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

    Text Solution

    |

  11. If f(x)=cos^(2)x+cos^(2)(x+(pi)/(3))+sinxsin(x+(pi)/(3)) and g((5)/(4)...

    Text Solution

    |

  12. If f(x)=10cosx+(13+2x)sinx then f'(x)+f(x)=

    Text Solution

    |

  13. If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (...

    Text Solution

    |

  14. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

    Text Solution

    |

  15. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

    Text Solution

    |

  16. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

    Text Solution

    |

  17. If y=logu|cos4x|+|sinx|,where u=sec2x find (dy)/(dx) at x=-pi/6

    Text Solution

    |

  18. If f(4)=4,f'(4)=1, then lim(x in4) (2-sqrt(f(x)))/(2-sqrt(x)) is equal...

    Text Solution

    |

  19. if 2x^2-3xy+y^2+x+2y-8=0 then (dy)/(dx)

    Text Solution

    |

  20. If y=log{((1+x)/(1-x))^(1//4)}-(1)/(2)tan^(-1)x," then "(dy)/(dx)=

    Text Solution

    |