Home
Class 11
MATHS
If y= sqrt ( x) + (1)/( sqrtx ), prove t...

If `y= sqrt ( x) + (1)/( sqrtx )`, prove that `2x (dy)/( dx ) + y=2 sqrt (x )`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ICSE|Exercise EXERCISE 19 (c )|21 Videos

  • DIFFERENTIATION

    ICSE|Exercise EXERCISE 19 (d)|25 Videos

  • DIFFERENTIATION

    ICSE|Exercise EXERCISE 19 (a)|12 Videos

  • CORRELATION ANALYSIS

    ICSE|Exercise Multiple Choice Question |7 Videos

  • ELLIPSE

    ICSE|Exercise CHAPTER TEST|10 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

If y=e^x+e^-x , prove that (dy)/(dx)=sqrt(y^2-4)

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

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

If y=sqrt(x)+1/(sqrt(x)),p rov et h a t2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

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

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

ICSE-DIFFERENTIATION-EXERCISE 19 (b)
  1. Differentiate the following functions: (7)/( x^( (2)/(3) ) )

    Text Solution

    |

  2. Differentiate the following functions: ( sqrt(x) + (1)/( sqrt( x) )...

    Text Solution

    |

  3. Differentiate the following functions: sqrt( x ) - (1)/( sqrt x) , ...

    Text Solution

    |

  4. Differentiate the following functions: 10. (1)/( x) + (3)/( x^2) + ...

    Text Solution

    |

  5. Differentiate the following functions: 11. 2x^((1)/(2)) + 6x^((1)/(3...

    Text Solution

    |

  6. Differentiate the following functions: 12. 8x^(3) - x^(2) + 5 - (2)/...

    Text Solution

    |

  7. Differentiate the following functions: 13. (3 x^7 + x^5 - 2x^4 + x-3...

    Text Solution

    |

  8. Differentiate the following functions: 14. (i) (2x-3)^(2) (ii) (2x -...

    Text Solution

    |

  9. Differentiate the following functions: 15. sqrt ( 3 x +2).

    Text Solution

    |

  10. Differentiate the following functions: Given f(x) = (7)/(4) x^(2), f...

    Text Solution

    |

  11. Find the derivative with respect to x of the following: (i) x - (1)/...

    Text Solution

    |

  12. Find the derivative with respect to x of the following: (ii) sqrt ( ...

    Text Solution

    |

  13. Find the derivative with respect to x of the following: (iii) 3x^(2)...

    Text Solution

    |

  14. Find the derivative with respect to x of the following: (iv) (x^2 + ...

    Text Solution

    |

  15. Find the derivative with respect to x of the following: (2x +x^4)/(...

    Text Solution

    |

  16. Find the derivative with respect to x of the following: (1+x^2)/( x^...

    Text Solution

    |

  17. If y= x + (1)/(x), prove that x^2 (dy)/( dx ) - xy + 2 =0

    Text Solution

    |

  18. If y= sqrt ( x) + (1)/( sqrtx ), prove that 2x (dy)/( dx ) + y=2 sqrt ...

    Text Solution

    |

  19. If y= (1)/( a-z), show that (dz)/( dy) = (z-a)^(2)

    Text Solution

    |

  20. If y= 1+ x + (x^2)/( 2!) + (x^3)/( 3!) + (x^4)/(4!) +…. to oo, show th...

    Text Solution

    |