Home
Class 12
MATHS
The differential coefficient of sin^(-1)...

The differential coefficient of `sin^(-1)((5cos x-4s in x)/(sqrt(41)))` is `-2` b.`-1` c. `1` d. `2`

A

`-2`

B

`-1`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
Let `u=sin^(-1)((4)/(5)sin2x+(3)/(5)cos2x)=sin^(-1)sin(alpha+2x).`
where `sin alpha=(3)/(5), cos alpha=(4)/(5)`
i.e., `u=alpha+2x.`
Similary, `y=cos^(-1)((5cos x-4 sinx)/(sqrt(41)))`
`=cos^(-1)cos(beta+x),`
Here, `cos beta=(5)/(sqrt(41)), sin beta=(4)/(sqrt(41))`
i.e., `v=beta+x`
`therefore" "(du)/(dv)=((du)/(dx))/((dv)/(dx))=(2)/(1)=2.`
Promotional Banner

Topper's Solved these Questions

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

  • MATRICES

    CENGAGE|Exercise Solved Examples And Exercises|165 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

Similar Questions

Explore conceptually related problems

Differentiate sin ^(-1) ((2 cos x + 3 sin x )/(sqrt(13))) w.r.to x

DIfferential coefficient of tan^-1(x/(1+sqrt(1-x^2)))w.r.t sin^-1x is

Differentiate cos^(^^)(-1){(cos x+sin x)/(sqrt(2))},-pi/4

Differential coefficient of sin^(-1)x w.r.t. cos^(-1)sqrt(1-x^2) is equal to......

The differential coefficient of sin^(-1)((4sin2x+3cos2x)/(5)) with respect to cos^(-1)((5cos x-4sin x)/(sqrt(41))) is -2b*-1c.1d

The differential coefficient of sin^(-1)((x)/(sqrt(1+x^(2)))) w.r. t cos^(-1)((1-x^(2))/(1+x^(2))) is -

Differentiate (sin x)^(5)+sin^(-1)sqrt(x)

If y= sin ^(-1) ((4cos x +5sin x )/( sqrt(41))) ,then (dy)/(dx)=

Differential coefficient of tan^(-1)((x)/(1+sqrt(1-x^(2)))) with respect to sin^(-1)x is (A) (1)/(2)(B)1(C)2 (D) (3)/(2)

Differential coefficient of sec(tan^(-1)x) is (x)/(1+x^(2))( b) x sqrt(1+x^(2))(c)(1)/(sqrt(1+x^(2))) (d) (x)/(sqrt(1+x^(2)))

CENGAGE-METHODS OF DIFFERENTIATION-Single Correct Answer Type
  1. The derivative of the function represented parametrically as x=2t=|...

    Text Solution

    |

  2. If y = tan^(-1)(u/sqrt(1-u^2)) and x = sec^(-1)(1/(2u^2-1)), u in (0...

    Text Solution

    |

  3. The differential coefficient of sin^(-1)((5cos x-4s in x)/(sqrt(41))) ...

    Text Solution

    |

  4. x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn= 1 b.2 c. 3 d. 4

    Text Solution

    |

  5. If x+y=3e^2t h e d/(dx)(x^y)=0forx= e^2 b. e^e c. e d. 2e^2

    Text Solution

    |

  6. If f(x)=(x-1)^(100)(x-2)^(2(99))(x-3)^(3(98))…(x-100)^(100), then the ...

    Text Solution

    |

  7. The function f: RvecR satisfies f(x^2)dotf^(x)=f^(prime)(x)dotf^(prime...

    Text Solution

    |

  8. The second derivative of a single valued function parametrically repre...

    Text Solution

    |

  9. For the curve sinx+siny=1 lying in first quadrant. If lim(xrarr0) x^(...

    Text Solution

    |

  10. If y=((alphax+beta)/(gammax+delta)), then 2(dy)/(dx).(d^(3)y)/(dx^(3))...

    Text Solution

    |

  11. If f(1)=3, f'(1) = 2, f''(1)=4, then (f^-)''(3)= (where f^-1=invers...

    Text Solution

    |

  12. If the third derivative of (x^(4))/((x-1)(x-2)) is (-12k)/((x-2)^(4))+...

    Text Solution

    |

  13. (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

    Text Solution

    |

  14. If R=([1+((dy)/(dx))^2]^(-3//2))/((d^2y)/(dx2)) , thenR^(2//3) can be ...

    Text Solution

    |

  15. x= 2 cos t -cos 2t ,y=2 sin t-sin 2t

    Text Solution

    |

  16. If y^3-y=2x ,t h e n(x^2-1/(27))(d^2y)/(dx^2)+x(dy)/d= y b. y/3 c. y/...

    Text Solution

    |

  17. Let f(x)=(g(x))/x w h e nx!=0 and f(0)=0. If g(0)=g^(prime)(0)=0a n d...

    Text Solution

    |

  18. Let f:(-oo,oo)vec[0,oo) be a continuous function such that f(x+y)=f(x)...

    Text Solution

    |

  19. Let f:R to R be a function satisfying f(x+y)=f(x)=lambdaxy+3x^(2)y^(2)...

    Text Solution

    |

  20. A functionf: Rvec[1,oo) satisfies the equation f(x y)=f(x)f(y)-f(x)-f(...

    Text Solution

    |