Home
Class 12
MATHS
tan^(-1)((5x+1)/(3-x-6x^(2)))...

`tan^(-1)((5x+1)/(3-x-6x^(2)))`

Text Solution

Verified by Experts

` y = tan^(-1) ((5x +1)/(3-x-6x^(2)))`
` = tan^(-1) [(5x+1)/(1-(6x^(2)+x-2))]`
` = tan^(-1) [((2x-1)+(3x+2))/(1-(2x-1)(3x+2))]`
` :. " " y = tan^(-1) (2x-1) + tan^(-1) (3x+2)`
` :. " " (dy)/(dx) = 1/(1+(2x-1)^(2)) d/(dx) (2x -1)+ 1/(1+(3x+2)^(2))*d/dx (3x +2)`
` = 1/(1+(2x-1)^(2)) xx 2 + 1/(1+(3x+2)^(2)) xx 3`
` :. " " (dy)/(dx) = 2/(1+(2x-1)^(2)) + 3/(1+(3x+2)^(2))`
Promotional Banner

Topper's Solved these Questions

  • MARCH 2018

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION - II|20 Videos

  • MARCH 2017

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION-II|20 Videos

  • MARCH 2019

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION-D|13 Videos

Similar Questions

Explore conceptually related problems

y= tan^(-1)((5-x)/(6x^(2)-5x-3)) find dy/dx

Differentiate tan^(-1){(5x)/(1-6x^(2))}-(1)/(sqrt(6))

tan^(-1)((6x)/(1+16x^(2)))

tan^-1((5x)/(1-6x^2))

Fin d (dy)/(dx) ify =tan^(-1)((6x)/(1-5x^(2))) dy,1 Find if y=tan1-5x2

Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))=tan^(-1)2x;|2x|<(1)/(sqrt(3))

Given that , tan^(-1) ((2x)/(1-x^(2))) = {{:(2 tan^(-1) x"," |x| le 1),(-pi +2 tan^(-1)x","x gt 1),(pi+2 tan^(-1)x"," x lt -1):} sin^(-1)((2x)/(1+x^(2))) ={{:(2 tan^(-1)x","|x|le1),(pi -2 tan^(-1)x","x gt 1 and ),(-(pi+2tan^(-1))","x lt -1):} sin^(-1) x + cos^(-1) x = pi//2 " for " - 1 le x le 1 If cos^(-1). (6x)/(1 + 9x^(2)) = - pi/2 + 2 tan^(-1) 3x" , then " x in

(d)/(dx)[tan^(-1)((6x)/(1+7x^(2)))]+(d)/(dx)[tan^(-1)((5+2x)/(2-5x))]=

Find the sum of each of the following series: (i) 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))...... upto n.

GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- MARCH 2018-SECTION - II
  1. Let the p.m.f. of a random variable X be - P(x) = (3 -x)/10 " for ...

    Text Solution

    |

  2. if int0^k (dx)/(2+8x^2)=pi/16 then find the value of k

    Text Solution

    |

  3. Integrating factor of linear differential equation x(dy)/(dx) + 2y = ...

    Text Solution

    |

  4. Evaluate : int e^(x) [(cos x - sin x)/(sin^(2) x)] dx.

    Text Solution

    |

  5. if y = tan^(2) (log x^(3))," find " (dy)/(dx).

    Text Solution

    |

  6. Find the area of ellipse x^(2)/1 + y^(2)/4 = 1.

    Text Solution

    |

  7. Obtain the differential equation by eliminating the arbitrary constant...

    Text Solution

    |

  8. Given X~ B (n,P) If n= 10 and p=0.4 , find E(X) and Var (X) .

    Text Solution

    |

  9. Evaluate : int 1/(3+2 sin x + cos x) dx.

    Text Solution

    |

  10. If x=acos^(3)t,y=asin^(3)t,"show that "(dy)/(dx)=-((y)/(x))^((1)/(3))

    Text Solution

    |

  11. Examine the contionuity of the following functions at the give points ...

    Text Solution

    |

  12. Find all the points of local maxima and minima and the correspondin...

    Text Solution

    |

  13. Prove that : int 1/(a^(2)-x^(2)) dx = 1/(2a) log |(a+x)/(a-x)|+c.

    Text Solution

    |

  14. int(-a)^(a)f(x)dx= 2int(0)^(a)f(x)dx, if f is an even function 0, if...

    Text Solution

    |

  15. If f(x)(x^(2)-9)/(x-3)+alpha, "for" x gt 3 =5, "for" x =3 =2x^(2)+...

    Text Solution

    |

  16. tan^(-1)((5x+1)/(3-x-6x^(2)))

    Text Solution

    |

  17. A fair coin is tossed 8 times. Find the probability that it shows head...

    Text Solution

    |

  18. Verify Rolle's theorem for the following function :f(x)=x^2-4x+10 on [...

    Text Solution

    |

  19. Find the particular solutions of the following differential equation :...

    Text Solution

    |

  20. Find the variance and standard deviation of the random variable X wh...

    Text Solution

    |