Home
Class 12
MATHS
Prove that d/(dx){x/2sqrt(a^2-x^2)+(a^2)...

Prove that `d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)}=sqrt(a^2-x^2)`

Text Solution

AI Generated Solution

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

Prove that: d/(dx)[x/2\ sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)]=sqrt(a^2-x^2)

P rov et h a t d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a) }=sqrt(a^2-x^2)

Differentiate the following w.r.t.x. (sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)-x^(2))-sqrt(a^(2)-x^(2)))

Differentiate tan^(-1)(x/(sqrt(1-x^2))) with respect to sin^(-1)(2xsqrt(1-x^2)), if -1/(sqrt(2)) < x< 1 /(sqrt(2))

Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to tan^(-1)(x/(sqrt(1-x^2))) .

Differentiate sin^(-1)sqrt(1-x^2) with respect to cot^(-1)(x/sqrt(1-x^2)) if 0< x <1

Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))} with respect to cos^(-1)x^2

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))) .

Differentiate tan^(-1)x/(1+sqrt((1-x^2))) +{2tan^(-1)sqrt(((1-x)/(1+x)))}sinwdotrdottdotxdot

Differentiate each of the following functions with respect to x : (i) sin^(-1)(2xsqrt(1-x^2)),-1/(sqrt(2))ltxlt1/(sqrt(2)) (ii) cos^(-1)(2x(sqrt(1-x^2)),-1/sqrt(2)ltxlt1/sqrt2

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=e^x+e^-x, prove that (dy)/(dx)=sqrt(y^2-4)

    Text Solution

    |

  2. If x y=4,prove , x((dy)/(dx)+y^2)=3y

    Text Solution

    |

  3. Prove that d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)}=sqrt(a^2-x^2)

    Text Solution

    |

  4. Differentiate the following with respect to x : cos^(-1)(sinx) and cot...

    Text Solution

    |

  5. If y=sin^(-1)((2x)/(1+x^2))+sec^(-1)((1+x^2)/(1-x^2)),0ltxlt1, prove t...

    Text Solution

    |

  6. Differentiate the following function with respect to x : tan^(-1)(...

    Text Solution

    |

  7. If y=cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))}...

    Text Solution

    |

  8. Find (dy)/(dx), when x=(e^t+e^(-t))/2 \ a n d \ y=(e^t-e^(-t))/2

    Text Solution

    |

  9. Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(si...

    Text Solution

    |

  10. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

    Text Solution

    |

  11. Differentiate the following function with respect to x : tan^(-1)(...

    Text Solution

    |

  12. Find (dy)/(dx), when x=(3a t)/(1+t^2)" and "y =(3a t^2)/(1+t^2)

    Text Solution

    |

  13. Differentiate the following function with respect to x : tan^(-1)(...

    Text Solution

    |

  14. Find (dy)/(dx), y=e^x+10^x+x^x

    Text Solution

    |

  15. Differentiate the following function with respect to x : tan^(-1){...

    Text Solution

    |

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

    Text Solution

    |

  17. Differentiate the following function with respect to x:sin(x^x)

    Text Solution

    |

  18. Differentiate the following function with respect to x : (logx)^(logx)

    Text Solution

    |

  19. Differentiate the following function with respect to x: 10^(logsin...

    Text Solution

    |

  20. If y=logsqrt((1+tanx)/(1-tanx)),"Prove that " (dy)/(dx)=sec2x

    Text Solution

    |