Home
Class 12
MATHS
If x=f(t)cost-f^(prime)(t)sint and y=f(t...

If `x=f(t)cost-f^(prime)(t)sint` and `y=f(t)sint+f^(prime)(t)cost ,` then `((dx)/(dt))^2+((dy)/(dt))^2=` (a)`f(t)-f^(primeprime)(t)` (b) `{f(t)-f^(primeprime)(t)}^2` (c) `{f(t)+f^(primeprime)(t)}^2` (d) none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|406 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

If x=f(t )cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f^(primeprime)(x)=f(x)=0 (b) 4f^(primeprime)(x)+f(x)=0 (c) f^(primeprime)(x)+f(x)=0 (d) 4f^(primeprime)(x)-f(x)=0

If F(x)=f(x)dotg(x) and f^(prime)(x)dotg^(prime)(x)=c , prove that (F^(primeprime))/F=f^(primeprime)/f+g^(primeprime)/g+(2c)/(fg)&F^(primeprimeprime)/F=f^(primeprimeprime)/f+g^(primeprimeprime)/g

Let f(t)="ln"(t) . Then, (d)/(dx)(int_(x^(2))^(x^(3))f(t)" dt")

If f(x)=3-2x+x^(2) , then ((f(x+t)-f(x))/(t)) =

A function f(x) satisfies f(x)=sinx+int_0^xf^(prime)(t)(2sint-sin^2t)dt is

If f(x)=int_0^x(sint)/t dt ,x >0, then

If f(x)=t^(2)+(3)/(2)t , then f(q-1)=

If F(x) =(1)/(x^(2))overset(x)underset(4)int [4t^(2)-2F'(t)]dt then F'(4) equals

Let f(x)=int_(0)^(x)(sin^(100)t)/(sin^(100)t+cos^(100)t)dt , then f(2pi)=

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)ddot(cosn x+isinn x) a...

    Text Solution

    |

  2. If y=asinm x+bcosm x , then find dy/dx

    Text Solution

    |

  3. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (...

    Text Solution

    |

  4. If y=tan^(-1){((log)e(e//x^2))/((log)e(e x^2))}+tan^(-1)((3+2\ (log)e ...

    Text Solution

    |

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

    Text Solution

    |

  6. If y=acos((log x)+bsin((log x) , then find dy/dx

    Text Solution

    |

  7. If x=2 and y=a t^2 ,then find dy/dx

    Text Solution

    |

  8. If x=f(t) and y=g(t) , then find (dy)/(dx)

    Text Solution

    |

  9. If y=sin(m\ sin^(-1)x) , then (1-x^2)y2-x y1 is equal to m^2y (b) m y ...

    Text Solution

    |

  10. If y=(sin^(-1)x)^2,\ then (1-x^2)y2 is equal to x y1+2 (b) x y1-2 (c)...

    Text Solution

    |

  11. If y=e^(tanx) , then (cos^2x)y2-(1+sin2x)y1=0

    Text Solution

    |

  12. If y=2/(sqrt(a^2-b^2)){tan^(-1)sqrt((a-b)/(a+b))tan(x/2)} , then show ...

    Text Solution

    |

  13. If y=(a x+b)/(x^2+c), prove that (2x y1+y)y3=3(x y2+y1)y2.

    Text Solution

    |

  14. If y=loge(x/(a+b x))^x , then x^3y2 is (a) (x y1-y)^2 (b) (1+y)^2 ...

    Text Solution

    |

  15. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

    Text Solution

    |

  16. If y^(1/n)+y^(-1/n) = 2x then (x^2-1)y2+xy1 is equal to

    Text Solution

    |

  17. differentiate y= sinx +logx with respect to x

    Text Solution

    |

  18. If y=xlogx then find dy/dx

    Text Solution

    |

  19. find dy/dx if x y-(log y)=1

    Text Solution

    |

  20. If y^2=a x^2+b x+c , then find (dy)/(dx)

    Text Solution

    |