Home
Class 12
MATHS
If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=...

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

Text Solution

AI Generated Solution

To solve the problem, we start with the equation given: \[ e^{y(x+1)} = 1 \] ### Step 1: Take the natural logarithm of both sides Taking the natural logarithm (ln) of both sides, we have: \[ \ln(e^{y(x+1)}) = \ln(1) \] ...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|406 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot

If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot

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

If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If y=a e^(2x)+b e^(-x) , show that, (d^2y)/(dx^2)-(dy)/(dx)-2y=0 .

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

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

If y=cotx show that (d^2y)/(dx^2)+2y(dy)/(dx)=0 .

If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2dot

If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2dot

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

    Text Solution

    |

  2. If y^3-y=2x , prove that (d^2y)/(dx^2)=-(24 y)/((3y^2-1)^3) .

    Text Solution

    |

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

    Text Solution

    |

  4. If y=x^x , find (d^2y)/(dx^2) .

    Text Solution

    |

  5. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

    Text Solution

    |

  6. If y=log{x+ sqrt( x^2+a^2 )} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy...

    Text Solution

    |

  7. If y=sin^(-1)x , then show that (1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0 .

    Text Solution

    |

  8. If y=e^m\ sin^((-1)x) , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2...

    Text Solution

    |

  9. If y={x+sqrt(x^2+1)}^m , show that (x^2+1)y2+x y1-m^2\ y=0

    Text Solution

    |

  10. If y=(sin^(-1)x)/(sqrt(1-x^2)) , show that (1-x^2)(d^2y)/(dx^2)-3x(dy)...

    Text Solution

    |

  11. If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .

    Text Solution

    |

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

    Text Solution

    |

  13. Find (d^2y)/(dx^2) , if x=a t^2,\ \ y=2a t .

    Text Solution

    |

  14. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

    Text Solution

    |

  15. If x=asint and y=a(cost+log tan(t/2) ) , find (d^2y)/(dx^2) .

    Text Solution

    |

  16. lf x=acostheta+bsintheta, y=asintheta-bcostheta then show that y^2(d^...

    Text Solution

    |

  17. If x=sint,y=sinpt, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2 y=...

    Text Solution

    |

  18. If x=sintheta , y=cosptheta , prove that (1-x^2)y2-x y1+p^2y=0 , where...

    Text Solution

    |

  19. If (x-a)^2+(y-b)^2=c^2, for some c >0, prove that([1+((dy)/(dx))^2]^(...

    Text Solution

    |

  20. If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...

    Text Solution

    |