Home
Class 12
MATHS
If y=tan^(-1)((2x)/(1-x^2))+sec^(-1)((1+...

If `y=tan^(-1)((2x)/(1-x^2))+sec^(-1)((1+x^2)/(1-x^2))` , `x >0` , prove that `(dy)/(dx)=4/(1+x^2)` .

Text Solution

Verified by Experts

Given `y=\sin ^{-1}((2x) /(1+x^{2}))+\sec ^{-1}((1+x^{2}) /(1-x^{2}))` $$ \text{Put} x=\tan \theta\\ \theta=\tan ^{-1} x\\ $$ ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

If y=sin^(-1)((2x)/(1+x^2))+sec^(-1)((1+x^2)/(1-x^2)), 0

If y=sin^(-1)((2x)/(1+x^(2)))+sec^(-1)((1+x^(2))/(1-x^(2))),0

if y=tan^(-1)((2x)/(1-x^(2))) then prove that (dy)/(dx)=(2)/(1+x^(2))

If y=sin^(-1)(x/(sqrt(1+x^2)))+cos^(-1)(1/(sqrt(1+x^2))), 0

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

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

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

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

If y=tan ^(-1) ((a-x) /(1+x^(2))),then (dy)/(dx) =

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate cot^(-1)((1-x)/(1+x)) with respect to x .

    Text Solution

    |

  2. If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]...

    Text Solution

    |

  3. If y=tan^(-1)((2x)/(1-x^2))+sec^(-1)((1+x^2)/(1-x^2)) , x >0 , prove t...

    Text Solution

    |

  4. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

    Text Solution

    |

  5. If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],find(dy)/(dx)

    Text Solution

    |

  6. If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),\ \ 0<x<1/2 , find (dy)/(dx) .

    Text Solution

    |

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

    Text Solution

    |

  8. If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),-1/2<x<0 , find (dy)/(dx)

    Text Solution

    |

  9. If y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(d...

    Text Solution

    |

  10. If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

    Text Solution

    |

  11. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

    Text Solution

    |

  12. If a x^2+2\ h x y+b y^2+2\ gx+2\ fy+c=0 , find (dy)/(dx) and (dx)/(dy)...

    Text Solution

    |

  13. If x^2+2x y+y^3=42 , find (dy)/(dx)

    Text Solution

    |

  14. If x^3+y^3=3a x y , find (dy)/(dx)

    Text Solution

    |

  15. If log\sqrt((x^2+y^2))=tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y)

    Text Solution

    |

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

    Text Solution

    |

  17. If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xd...

    Text Solution

    |

  18. If siny=xsin(a+y), prove that (dy)/(dx)=(s in^2(a+y))/(sina) .

    Text Solution

    |

  19. If sqrt(1-x^6)+sqrt(1-y^6)=a^3(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/...

    Text Solution

    |

  20. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/(t^2) , then prove that (dy)/(dx)=1...

    Text Solution

    |