Home
Class 12
MATHS
If y = (x - 2 )/ (x + 2) , show that ...

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

Text Solution

Verified by Experts

The correct Answer is:
`2x (dy)/(dx) = 1-((x-2)/(x + 2))^(2) = 1 - y^(2) [becausey = (x- 2 )/(x+ 2 )]`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Multiple Choice Type Questions|14 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Very short Answer Type Questions|38 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy

If y = x/(x+a) ,show that x dy/dx = y (1- y)

If tan y = (tan x+sec x-1)/(tanx -sec x+1) show that (dy)/(dx) = 1/2

If y^2 (1-x^2) = x^2 +1 , show that (1-x^4) (dy/dx)^2 = y^4 -1 .

(dy)/(dx)=(2x-3y)/(3x-2y)

If y = x + (x^(3))/(3)+(x^(5))/(5)+* * * show that (dy)/(dx) = (1) /(1 - x^(2)) .

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

If e^(y)(x+1)=1 , show that (d^(2)y)/(dx^(2)) = ((dy)/(dx))^(2) .

If y=x+(x^(3))/(3)+(x^(5))/(5)+…oo , show that (dy)/(dx)=(1)/(1-x^(2)) .

If y=e^((y)/(x)) show that, (dy)/(dx)=(y^(2))/(x(y-x)) .

CHHAYA PUBLICATION-DIFFERENTIATION-Example
  1. Find (dy)/(dx) , when y = sqrt(x) log x* 10^(x)

    Text Solution

    |

  2. Find (dy)/(dx) y= sqrt(x) sec x tan x

    Text Solution

    |

  3. If f(x+y) = f(x) * f(y) for all real x and y and f(5)=2,f'(0) = 3 ,...

    Text Solution

    |

  4. If f (a) = 2 , f'(a) = 1, g (a) = -1 and g'(a) = 2 , show tha...

    Text Solution

    |

  5. Find the derivatives of the following functions w.r.t. x : y = (si...

    Text Solution

    |

  6. Find the derivatives of the following functions w.r.t.x : y=(x^...

    Text Solution

    |

  7. Find the derivatives of the following functions w.r.t.x : (cot x + ...

    Text Solution

    |

  8. Find the derivatives of the following functions w.r.t.x : (x sin ...

    Text Solution

    |

  9. If h(x) = [ f (x) ] ^(2) + [ g (x) ] ^(2) and (x) = g (x), f''(x)...

    Text Solution

    |

  10. If y = 2 x^(3)- 15 x^(2) + 36 x + 8 , slove the equation (dy)/(dx)=...

    Text Solution

    |

  11. If y = sqrt(3x)-sqrt(3/(x))+(x + 6) /(6 - x ) find the value of ((d...

    Text Solution

    |

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

    Text Solution

    |

  13. If f(x) = (6-4x)/(1+2x+2x^(2)) find f'(x) . Also find the value of...

    Text Solution

    |

  14. If y = x + (x^(3))/(3)+(x^(5))/(5)+* * * show that (dy)/(dx) = (1...

    Text Solution

    |

  15. Find the value of a, If f(x) = a |sin x | + 2x is differentiable ...

    Text Solution

    |

  16. Find the value of (d)/(dx)[(cos (x - alpha))/(sin x )] .

    Text Solution

    |

  17. If y = 1 + x + (x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+* * * +(x^(n))...

    Text Solution

    |

  18. If y = sqrt(x/(m))+sqrt(m/(x)) show that 2xy (dy)/(dx) = (x)/(m) - ...

    Text Solution

    |

  19. If x in (0, (pi)/(2))cup((pi)/(2),pi) and y = sqrt((1 + cos 2 x )...

    Text Solution

    |

  20. If f(x) = |x|+|x - 1| then find f'(x),

    Text Solution

    |