Home
Class 12
MATHS
If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),...

If `y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),-1/2

Text Solution

Verified by Experts

`y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2)`
`2x=costheta`
`y=cos^(-1)(costheta)+2cos^(-1)sqrt(1-cos^2theta)`
=`theta+2cos^(-1)sintheta`
=`theta+2cos^(-1)cos(pi/2-theta)`
y=`pi-theta`
y=`pi-cos^(-1)2x`
`dy/dx=2/sqrt(1-4x^2)`
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=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2), 0

cos^-1((x)/sqrt(1+x^2))

cos^(-1)(sqrt(1+cos x)/2)

3cos^(-1)x=sin^(-1)(sqrt(1-x^(2))(4x^(2)-1))

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

underset0 If y=cos^(-1){x sqrt(1-x)+sqrt(x)sqrt(1-x^(2))} and

If y=(x cos^(-1)x)/(sqrt(1-x^(2)))-log sqrt(1-x^(2)), then prove that (dy)/(dx)=(co^(1-x)x)/((1-x^(2))^((3)/(2)))

The number of real solution of cot^(-1)sqrt(x(x+4))+cos^(-1)sqrt(x^(2)+4x+1)=(pi)/(2) is equal to

If y=cos^(-1){(2x-3sqrt(1-x^(2)))/(sqrt(13))}, find (dy)/(dx)

cos^(-1)((2sqrt(x))/(1+x))

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],find(dy)/(dx)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Differentiate cos^(-1)(1-2x^2) with respect to x , if 0<x<1 (ii) -1<x...

    Text Solution

    |

  7. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)),if -1/sqrt(3)ltxlt1 /sqrt...

    Text Solution

    |

  8. Differentiate each of the following functions with respect to x : (i)...

    Text Solution

    |

  9. Differentiate the following function with respect to x : sin^(-1)(si...

    Text Solution

    |

  10. Differentiate sin^(-1)(2xsqrt(1-x^2))w i t hr e s p e c ttox ,if -1/(...

    Text Solution

    |

  11. Differentiate sin^(-1)(3x-4x^3)

    Text Solution

    |

  12. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

    Text Solution

    |

  13. If y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)} and 0<x<1 find (dy)/(dx)

    Text Solution

    |

  14. If y=sqrt(a^2-x^2) , prove that y(dy)/(dx)+x=0

    Text Solution

    |

  15. If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

    Text Solution

    |

  16. If y=sqrt(x^2+a^2) ,prove that y(dy)/(dx)-x=0

    Text Solution

    |

  17. If y=xsin^(-1)x+sqrt(1-x^2), p rov et h a t(dy)/(dx)=sin^(-1)x

    Text Solution

    |

  18. If y=1/2log((1-cos2x)/(1+cos2x)),p rov et h a t(dy)/(dx)=2cos e c2x

    Text Solution

    |

  19. If y=e^xcosx ,p rov et h a t(dy)/(dx)=sqrt(2)e^xcos(x+pi/4)

    Text Solution

    |

  20. If y=(x-1)log(x-1)-(x+1)log(x+1),p rov et h a t(dy)/(dx)=log((x-1)/(1+...

    Text Solution

    |