Home
Class 12
MATHS
If y=(xcos^(-1)x)/(sqrt(1-x^2))-logsqrt(...

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

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

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

If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y), prove that (dy)/(dx)=sqrt((1-y^2)/(1-x^2))

If y= sin^(-1)(x/(sqrt(1+x^2))) + cos^(-1)(1/(sqrt(1+x^2))) , prove that (dy)/(dx)=(2x)/(1+x^2) .

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))

If y=x\ sin^(-1)x+sqrt(1-x^2) , prove that (dy)/(dx)=sin^(-1)x

If ysqrt(1-x^2)+xsqrt(1-y^2)=1," prove that "(dy)/(dx)= - sqrt((1-y^2)/(1-x^2))dot

If sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx) = sqrt((1-y^(2))/(1-x^(2)))

If sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx) = sqrt((1-y^(2))/(1-x^(2)))

If sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx) = sqrt((1-y^(2))/(1-x^(2)))

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Find (dy)/(dx) , when y=(sinx+x^2)/(cot2x)

    Text Solution

    |

  2. If y={x+sqrt(x^2+a^2)}^n , then prove that (dy)/(dx)=(n y)/(sqrt(x^2+a...

    Text Solution

    |

  3. If y=(xcos^(-1)x)/(sqrt(1-x^2))-logsqrt(1-x^2), then prove that (dy)/(...

    Text Solution

    |

  4. Differentiate sin(m\ sin^(-1)x) with respect to x :

    Text Solution

    |

  5. Differentiate (a^(sin^(-1)x))^2 with respect to x :

    Text Solution

    |

  6. Differentiate: e^(cos^(-1)sqrt(1-x^(2))

    Text Solution

    |

  7. Differentiate the following functions with respect to x : (log)(10)x...

    Text Solution

    |

  8. Differentiate 5^3-x^2+(3-x^2)^5 with respect to x :

    Text Solution

    |

  9. If y=(sqrt(a^2+x^2)+sqrt(a^2-x^2))/(sqrt(a^2+x^2)-sqrt(a^2-x^2)),s ho...

    Text Solution

    |

  10. If y=sqrt((1-x)/(1+x)) prove that (1-x^2)(dy)/(dx)+y=0

    Text Solution

    |

  11. If y=sqrt((1+e^x)/(1-e^x)),s howt h a t(dy)/(dx)=(e^x)/((1-e^x)sqrt(1...

    Text Solution

    |

  12. If (1+x)^n=c0+C1x+C2x^2++Cn x^n ,u s ingd e r i v a t i v e sp rov et ...

    Text Solution

    |

  13. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

    Text Solution

    |

  14. If f(x)=sqrt(x^2+1),\ \ g(x)=(x+1)/(x^2+1) and h(x)=2x-3 , then find f...

    Text Solution

    |

  15. Differentiate sin(3x+5) with respect to x :

    Text Solution

    |

  16. Differentiate t a n^2x with respect to x :

    Text Solution

    |

  17. Differentiate tan(x+45) with respect to x :

    Text Solution

    |

  18. Differentiate sin(logx) with respect to x :

    Text Solution

    |

  19. Differentiate e^(sinsqrt(x)) with respect to x :

    Text Solution

    |

  20. Differentiate e^(tanx) with respect to x :

    Text Solution

    |