Home
Class 12
MATHS
d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=...

`d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=`

A

`(1)/(2(1+x)sqrt(x))`

B

`(3)/((1+x)sqrt(x))`

C

`(2)/((1+x)sqrt(x))`

D

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

Text Solution

Verified by Experts

The correct Answer is:
`=(3)/(2sqrt(x)(1+x))`
`(d)/(dx)(tan^(-1)""(sqrt(x)(3-x))/(1-3x))`
`(d)/(dx)(tan^(-1)""((tan theta(3-tan^(2)theta)))/(1-3tan^(2)theta))`
`("putting "sqrt(x)=tan theta or theta=tan^(-1)sqrt(x))`
`=(d)/(dx)(tan^(-1)""((3tantheta-tan^(3)theta))/(1-3tan^(2)theta))`
`=(d)/(dx)[tan^(-1)(tan 3theta)]=(d)/(dx)(3theta)`
`=(d)/(dx)[3tan^(-1)sqrt(x)]=(3)/(2sqrt(x)(1+x))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

(d)/(dx)[tan^-1((sqrt(1+x^(2))-1)/(x))]=

(d)/(dx)(tan^(-1)((sqrt(x)-x)/(1+x^((3)/(2))))) equals- (x<=0)

(d)/(dx)tan^(-1)((sqrt(x)-x)/(1+x^((3)/(2))))=

(d)/(dx)tan^(-1)((x)/(1-sqrt(1+x^(2))))]=

(d)/(dx)(tan^(-1)(birth x))

(d)/(dx)[tan^(-1)((1)/(2x)-(x)/(2))]=

(d)/(dx)[tan^(-1)((x-sqrt(a^(2)-x^(2)))/(x+sqrt(a^(2)-x^(2))))]=

(d)/(dx)[sec(tan^(-1)x)]=

(d)/(dx)[tan^(-1)((12x-64x^(3))/(1-48x^(2)))]=

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to x+y...

    Text Solution

    |

  2. " If "y=sqrt(logx+sqrt(logx+sqrt(logx+...oo)))," then "(dy)/(dx) is

    Text Solution

    |

  3. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=

    Text Solution

    |

  4. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

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

    Text Solution

    |

  6. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

    Text Solution

    |

  7. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

    Text Solution

    |

  8. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

    Text Solution

    |

  9. If y=(x^x)^x then (dy)/(dx) is

    Text Solution

    |

  10. The first derivative of the function [cos^(-1)(sin sqrt((1+x)/2))+x^x]...

    Text Solution

    |

  11. f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)'...

    Text Solution

    |

  12. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  13. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  14. Suppose f(x)=e^(ax)+e^(bx)," where " a ne b, and that f''(x) -2f'(x)-1...

    Text Solution

    |

  15. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto 2^(20)(cos2x-2^(20)os3x...

    Text Solution

    |

  16. (d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d...

    Text Solution

    |

  17. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

    Text Solution

    |

  18. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

    Text Solution

    |

  19. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

    Text Solution

    |

  20. If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is

    Text Solution

    |