Home
Class 12
MATHS
If y=xsiny, prove that (dy)/(dx)=y/(x(1...

If `y=xsiny`, prove that `(dy)/(dx)=y/(x(1-xcosy)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If y=xsiny , prove that (dy)/(dx)=(siny)/((1-xcosy))

If y = x siny , prove that x.dy/dx = y / (1 - x cosy)

If x y=1 , prove that (dy)/(dx)+y^2=0 .

If y=x/(x+2) , prove that x(dy)/(dx)=(1-y)y

If (sinx)^y=x+y , prove that (dy)/(dx)=(1-(x+y)ycotx)/((x+y)logsinx-1)

If x=e^(x//y) , prove that (dy)/(dx)=(x-y)/(xlogx)

If y =(x)/(x+5) then prove that x (dy)/(dx)=y(1-y)

If y= (x)/( x+a) , prove that x (dy)/( dx) = y(1-y) .

If x=e^(x/y) ,prove that (dy)/(dx)=(x-y)/(xlogx)

If y^x=e^(y-x) , prove that (dy)/(dx)=((1+logy)^2)/(logy)

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=(ax^2)/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+c/(x-c)+1 then (y prim...

    Text Solution

    |

  2. If x=e^(x/y),prove that(dy)/(dx)=(x-y)/(xlogx)

    Text Solution

    |

  3. If y=xsiny, prove that (dy)/(dx)=y/(x(1-xcosy)

    Text Solution

    |

  4. If x ylog(x+y)=1, prove that (dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2+x+y))

    Text Solution

    |

  5. If (sin"x")^y=x+y ,p rov et h a t(dy)/(dx)=(1-(x+y)ycotx)/((x+y)logsin...

    Text Solution

    |

  6. Differentiate: (logx)^x+x^(logx)w i t hr e s p e c t to x :

    Text Solution

    |

  7. Find the derivative of (sqrt(x)(x+4)^(3/2))/((4x-3)^(4/3)) with respec...

    Text Solution

    |

  8. Differentiate the following functions with respect to x : (cos"x")^x ...

    Text Solution

    |

  9. Differentiate the following functions with respect to x : (i) (x^x...

    Text Solution

    |

  10. If y={(log)(cosx)sinx}{(log)(sinx)cosx}^(-1)+sin^(-1)((2x)/(1+x^2)),f...

    Text Solution

    |

  11. If sqrt(y+x)+sqrt(y-x)=c ,s howt h a t(dy)/(dx)=y/x-sqrt((y^2)/(x^2)-1...

    Text Solution

    |

  12. If y=cos^(-1)sqrt((cos3x)/(cos^3x)),t h e ns howt h a t(dy)/(dx)=sqrt...

    Text Solution

    |

  13. If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y),p rov et h a t(dy)/(dx)=sqrt((1-y^2...

    Text Solution

    |

  14. if x^2+y^2 = t - 1/t and x^4 + y^4 = t^2 + 1/t^2 then prove that dy/dx...

    Text Solution

    |

  15. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

    Text Solution

    |

  16. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

    Text Solution

    |

  17. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

    Text Solution

    |

  18. Differentiate the functions with respect to x : tan^(-1){(sqrt(1+a^2x...

    Text Solution

    |

  19. Differentiate the functions with respect to x : cos^(-1){(cosx+sinx...

    Text Solution

    |

  20. If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0, prove t...

    Text Solution

    |