Home
Class 12
MATHS
The function u=e^x sin x ; v=e^x cos x s...

The function `u=e^x sin x ; v=e^x cos x` satisfy the equation a.`v(d u)/(dx)-u(d v)/(dx)=u^2+v^2` b. `(d^2u)/(dx^2)=2v` c. `(d^2v)/(dx^2)=-2u` d. `(d u)/(dx)+(d v)/(dx)=2v`

A

`v(du)/(dx)-u(dv)/(dx)=u^(2)+v^(2)`

B

`v(d^(2)u)/(dx^(2))=2v`

C

`(d^(2)v)/(dx^(2))=-2u`

D

All of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|10 Videos

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|16 Videos

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise SOLVED EXAMPLES|7 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

The functions u=e^(x).sinx and v=e^(x).cosx satisfy the equation

If u=a x+b ,t h e n(d^n)/(dx^n)(f(a x+b)) is equal to a. (d^n)/(d u^n)(f(u)) b. a(d^n)/(d u^n)(f(u)) c. a^n(d^n)/(d u^n) f(u) d. a^(-n)(d^n)/(dx^n)(f(u))

If u=inte^(ax)sin " bx dx" and v=inte^(ax)cos " bx dx then "(u^(2)+v^(2))(a^(2)+b^(2))=

Differentiate each function by applying the basic rules of differentiation ((u)/(u-1)-(u)/(u+1))

If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt((1-u^2)/(1-v^2))

If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt((1-u^2)/(1-v^2))

Differentiate each function by applying the basic rules of differentiation ((2u)/(1-2u))

If (x+yi)^(3)=u + vi , prove that (u)/(x) +(v)/(y) = 4(x^(2)-y^(2))

A car moves from X to Y with a uniform speed v_u and returns to X with a uniform speed v_d . The average speed for this round trip is : (a) (2v_(d)v_(u))/(v_(d)+v_(u)) (b) sqrt(v_(u)u_(d)) (c) (v_(d)v_(u))/(v_(d)+v_(u)) (d) (v_(u)+v_(d))/(2)

If u=inte^(ax)sin " bx dx" and v=int(e^(ax))cos " bx dx" ,then tan^(-1)((u)/(v))+tan^(-1)((b)/(a)) equals

ARIHANT MATHS ENGLISH-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. Let f(x)=x^(n) , n being a non-negative integer, The value of n for w...

    Text Solution

    |

  2. If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the grea...

    Text Solution

    |

  3. The function u=e^x sin x ; v=e^x cos x satisfy the equation a.v(d u...

    Text Solution

    |

  4. If f(x)=log(x^(2))(logx),then f '(x)at x= e is

    Text Solution

    |

  5. Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for ...

    Text Solution

    |

  6. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

    Text Solution

    |

  7. "If "y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))))," then prove that "(dy)/(...

    Text Solution

    |

  8. If f(x)=|cosx-sinx| , then f'(pi/4) is equal to

    Text Solution

    |

  9. Let f(x)=x^2+xg^2(1)+g^''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then fin...

    Text Solution

    |

  10. if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) +...

    Text Solution

    |

  11. If y+log(1+x)=0 which of the following is true?

    Text Solution

    |

  12. If y=2^(3^(x)), then y' equals

    Text Solution

    |

  13. If g is the inverse of fandf(x) = x^(2)+3x-3,(xgt0). then g'(1) equal...

    Text Solution

    |

  14. If x^(3)-2x^(2)y^(2)+5x+y-5=0 and y(1) = 1, then

    Text Solution

    |

  15. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a)1/(2y-1)...

    Text Solution

    |

  16. Ify=x^((lnx)^ln(lnx)) , then (dy)/(dx) is equal to

    Text Solution

    |

  17. Which of the following functions are not derivable at x=0?

    Text Solution

    |

  18. "Let "f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1-1))x." Then"

    Text Solution

    |

  19. If 2^(x)+2^(y)=2^(x+y) then (dy)/(dx)is equal to

    Text Solution

    |

  20. For the function y=f(x)=(x^(2)+bx+c)e^(x), which of the following hold...

    Text Solution

    |