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)`
`dy/dx=-1/(sqrt(1-4x^2)) xx 2 -1/(x)xx1/(2(sqrt(1-4x^2)))xx-8x`
`dy/dx=-6/(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

If quad cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^(2)),-(1)/(2)

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)

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),\ \ 0<x<1/2 , find (dy)/(dx) .

    Text Solution

    |

  2. If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0 , prove ...

    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 y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(d...

    Text Solution

    |

  5. If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

    Text Solution

    |

  6. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

    Text Solution

    |

  7. If a x^2+2\ h x y+b y^2+2\ gx+2\ fy+c=0 , find (dy)/(dx) and (dx)/(dy)...

    Text Solution

    |

  8. If x^2+2x y+y^3=42 , find (dy)/(dx)

    Text Solution

    |

  9. If x^3+y^3=3a x y , find (dy)/(dx)

    Text Solution

    |

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

    Text Solution

    |

  11. If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((x+1)^2)

    Text Solution

    |

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

    Text Solution

    |

  13. If siny=xsin(a+y), prove that (dy)/(dx)=(s in^2(a+y))/(sina) .

    Text Solution

    |

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

    Text Solution

    |

  15. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/(t^2) , then prove that (dy)/(dx)=1...

    Text Solution

    |

  16. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

    Text Solution

    |

  17. If y=cos^(-1)sqrt((cos3x)/(cos^3x)),t h e ns howt h a t(dy)/(dx)=sqrt...

    Text Solution

    |

  18. If x y=c^2 , find (dy)/(dx)

    Text Solution

    |

  19. If y^3-3x y^2=x^3+3x^2\ y , find (dy)/(dx)

    Text Solution

    |

  20. If x^(2//3)+y^(2//3)=a^(2//3) , find (dy)/(dx)

    Text Solution

    |