Home
Class 12
MATHS
If x=costheta,ysin^3theta,"p r o v et h...

If `x=costheta,ysin^3theta,"p r o v et h a t"` `y(d^2y)/(dx^2)+((dy)/(dx))^2=3sin^2theta(5cos^2theta-1)dot`

A

` 3sin ^(2) theta (1-2 cos ^(2)theta) `

B

` 3sin ^(2)theta (2cos ^(2)theta -1)`

C

` 3sin ^(2)theta (1-5cos ^(2)theta )`

D

` 3sin ^(2) theta (5cos ^(2)theta -1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • Differential Equation

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTION|277 Videos
  • INTEGRATION

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|582 Videos

Similar Questions

Explore conceptually related problems

If x=cos theta,y sin^(3)theta, prove that y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=3sin^(2)theta(5cos^(2)theta-1)

If x=cos theta,y=s in^(3)theta, prove that y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=3s in^(2)theta(5cos^(2)theta-1)

If x=a(1-cos^3theta),y=asin^3theta,"p r o v et h a t"(d^2y)/(dx^2)=(32)/(27a) "at" theta=pi/6dot

If x=acos^3theta,y=a sin^3theta then find (d^2y)/(dx^(2))

If x=a cos theta,y=b sin theta, show that (d^(2)y)/(dx^(2))=-(b^(4))/(a^(2)y^(3))

If x=cos theta,y=sin5 theta then (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=

x=a sec theta,y=b tan theta,pr@v et h a t(d^(2)y)/(dx^(2))=-(b^(4))/(a^(2)y^(3))

If x=a cos^3theta,y=asin^3theta , then 1+((dy)/(dx))^2 is ___

If x=cos theta-cos2 theta,y=sin theta-sin2 theta then (dy)/(dx) is

NIKITA PUBLICATION-DIFFERENTIATION -MCQ
  1. If x= a sec theta ,y =a tan theta ,then " at " theta = (pi)/(4) ,(d^(...

    Text Solution

    |

  2. If x = sin theta, y = sin^(3) theta then (d^(2)y)/(dx^(2)) at theta = ...

    Text Solution

    |

  3. If x=costheta,ysin^3theta,"p r o v et h a t" y(d^2y)/(dx^2)+((dy)/(...

    Text Solution

    |

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

    Text Solution

    |

  5. If x=a sin theta ,y =bcos theta,then (d^(2)y)/(dx^(2))=

    Text Solution

    |

  6. If x = 2 cos t - cos 2t , y = 2 sin t - sin 2t, then the value of ...

    Text Solution

    |

  7. If x= asin t- b cos t ,y=a cost +bsin t,then y^(3) (d^(2) y)/(dx^(2) ...

    Text Solution

    |

  8. If x =theta -sin theta ,y=1-cos theta,then (d^(2)y)/(dx^(2))=

    Text Solution

    |

  9. if x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta) then (d^...

    Text Solution

    |

  10. If x= sin sqrtt,y =e^(sqrt( t) ),then (d^(2)y)/(dx^(2))=

    Text Solution

    |

  11. If x=sqrt(a^sin^((-1)t)), y=sqrt(a^cos^((-1)t)), show that (dy)/(dx)=-...

    Text Solution

    |

  12. The second order derivative of a sin^3 t w.r.t, a cos^3 t at t = pi/4...

    Text Solution

    |

  13. If x=log theta ,theta gt 0and y= (1)/( theta ),then (d^(2) y)/(dx^(2)...

    Text Solution

    |

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

    Text Solution

    |

  15. If x=f(t) and yy=g(t) are differentiable functions of t then (d^...

    Text Solution

    |

  16. (d^2x)/(d y^2) equals

    Text Solution

    |

  17. (d^2x)/(d y^2) equals

    Text Solution

    |

  18. Given f(x)=2x,xlt0=0,xge0,"then "f(x) is

    Text Solution

    |

  19. If g(x) is the inverse function of f(x) and f'(x)=(1)/(1+x^(4)), then ...

    Text Solution

    |

  20. If for x (0,1/4), the derivative of tan^(-1)((6xsqrt(x))/(1-9x^3)) is ...

    Text Solution

    |