Home
Class 12
MATHS
If y =tan ^(-1)((x ^(1//3) -a^(1//3))/(1...

If `y =tan ^(-1)((x ^(1//3) -a^(1//3))/(1+x ^(1//3)a ^(1//3))), x gt 0, a gt 0, then (dy)/(dx)` is:

A

`1/(x^(1//3)(1+x^(2//3)))`

B

`2/(x^(2//3)(1+x^(2//3)))`

C

`1/(3x^(2//3)(1+x^(2//3)))`

D

`1/(3x^(1//3)(1+x^(2//3)))`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL 2|103 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

Differentiate tan^(-1){(x^(1//3)+a^(1//3))/(1-(a x)^(1//3))} with respect to x

If tan ^(-1) ((1-x)/(1+x))= (1)/(2) tan^(-1) x, x gt 0 , then x = ?

If y = tan^(-1) ((1)/(x^(2) + x + 1)) + tan^(-1) ((1)/( x^(2) + 3x + 3)) + tan^(-1) ((1)/( x^(2) + 5x + 7))+ tan^(-1) ((1)/( x^(2) +7x + 13)), x gt 0 and ((dy)/( dx))_(x=0)= ( - k )/( 1+ k) then the value of k is

Let f (x)= {((1+ax )^(1//x), x lt 0),( ((x+c)^(1//3)-1)/((x+1)^(1//2) -1), x gt 0):}, is continous at x=0, then 3 (e ^(a)+b+c) is equal to:

If y = tan^(-1)( sqrt((x+1)/(x-1))) " for " |x| gt 1 " then " (dy)/(dx) =

Solve tan^(-1) ((1-x)/(1+x))= (1)/(2) tan^(-1) x(x gt 0)

y=tan^(-1) ((3x-x^3)/(1-3x^2)) . Find dy/dx .

If (x^(2) + 1)/(x)= 3(1)/(3) and x gt 1 , find x- (1)/(x)

If y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))ltxlt1 /(sqrt(3)), then find (dy)/(dx)

If y= "tan"^(-1) (4x)/(1+5x^(2)) + "tan"^(-1) (2 + 3x)/(3-2x) , then prove that (dy)/(dx)= (5)/(1+25x^(2))

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL -1
  1. Solve : log4(log3(log2x))=0

    Text Solution

    |

  2. If x = a cos^(3) theta, y = a sin ^(3) theta then sqrt(1+((dy)/(dx))^(...

    Text Solution

    |

  3. If y =tan ^(-1)((x ^(1//3) -a^(1//3))/(1+x ^(1//3)a ^(1//3))), x gt 0,...

    Text Solution

    |

  4. If x^2+x y+y^2=7/4, then (dy)/(dx) at x=1 and y=1/2 is:

    Text Solution

    |

  5. Let y=sqrt(x+sqrt(x+sqrt(x+...oo)))," then "(dy)/(dx) is equal to

    Text Solution

    |

  6. If f' (x) = sin (log x) and y = f((2x+3)/(3- 2x)), " then " (dy)/(...

    Text Solution

    |

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

    Text Solution

    |

  8. If x=sin theta and y=cos^(3) then 2y(d^(2)y)/(dx^(2))+4((dy)/(dx))^(2)...

    Text Solution

    |

  9. If u=3x^(12) and v=x^(6) then (du)/(dv) is

    Text Solution

    |

  10. If x=e^(-t^(2)), y=tan^(-1)(2t+1), then (dy)/(dx)=

    Text Solution

    |

  11. If x^y y^x=1 , prove that (dy)/(dx)=-(y(y+xlogy))/(x(ylogx+x))

    Text Solution

    |

  12. If x = t + (1)/(t) "and " y = t - (1)/(t) . "then" (dy)/(dx) is equa...

    Text Solution

    |

  13. Let f(x)=m ax{2 sin x,1-cosx},x epsilon (0,pi). Then set of points of ...

    Text Solution

    |

  14. Differential coefficient of (x^((1+m)/(m-n)))^((1)/(n-1)).(x^((m+n)/(l...

    Text Solution

    |

  15. Let f (x) be a polynomial in x. The second derivative of f (e ^(x)) w...

    Text Solution

    |

  16. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

    Text Solution

    |

  17. If f(x)=x^(n),"n" epsilon N, then the value of f(1)-(f^(')(1))/(1!)+(f...

    Text Solution

    |

  18. If y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , find (dy)/(...

    Text Solution

    |

  19. Find (dy)/(dx), if y=sin^(-1)[xsqrt(\ 1-x)-\ sqrt(x)\ sqrt(1-x^2)\ ]\

    Text Solution

    |

  20. If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t) satisfy f(x)((dy)/(dx))^(3)=...

    Text Solution

    |