Home
Class 12
MATHS
If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((d...

If `ln((e-1)e^(xy) +x^2)=x^2+y^2` then `((dy)/(dx))_(1,0)` is equal to

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

`"We have, "(e-1)e^(xy)+x^(2)=e^(x^(2))+y^(2)`
Differentiating both sides w.r.t. x, we get
`(e-1)cdote^(xy)cdot(xcdot(dy)/(dx)+y)+2x=e^(x^(2)+y^(2)).(2x+2y(dy)/(dx))`
Putting x=1 and y = 0, we get
`(e-1)((dy)/(dx))+2=e(2+0)`
`rArr" "((dy)/(dx))_((1,0))=2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

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

If xlog_e(log_ex)-x^2+y^2=4(ygt0)",then" dy//dx" at " x=e is equal to

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

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

(dy)/(dx) + 3y = e^(-2x)

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

(dy)/(dx) = e^(2x-y) + x^(3) e^(-y)

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

    Text Solution

    |

  2. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

    Text Solution

    |

  3. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

    Text Solution

    |

  4. If y=(x^x) then (dy)/(dx) is

    Text Solution

    |

  5. The first derivative of the function [cos^(-1)(s insqrt((1+x)/2))+x^x]...

    Text Solution

    |

  6. f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)'...

    Text Solution

    |

  7. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  8. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  9. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f prime prime(x...

    Text Solution

    |

  10. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto 2^(20)(cos2x-2^(20)os3x...

    Text Solution

    |

  11. (d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d...

    Text Solution

    |

  12. The nth derivative of the function f(x)=1/(1-x^2) [where x in(-1,1) a...

    Text Solution

    |

  13. If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a)(x(dy)/(dx)-y)^2 (b)...

    Text Solution

    |

  14. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

    Text Solution

    |

  15. If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y2+x y1 is (where yr represen...

    Text Solution

    |

  16. If (sinx)(cosy)=1/2,t h e n(d^2y)/(dx^2)a t(pi/4,pi/4) is -4 (b) -2 (c...

    Text Solution

    |

  17. A function f satisfies the condition f(x)=f^(prime)(x)+f^(x)+f^(x) ,w ...

    Text Solution

    |

  18. Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,...

    Text Solution

    |

  19. If y^2=a x^2+b x+c ,t h e ny^3(d^(2y))/(dx^2) is a constant a functio...

    Text Solution

    |

  20. If y=sinx+e^x ,t h e n(d^(2x))/(dy^2)= (-sinx+e^x)^(-1) (sinx-e^x)/(...

    Text Solution

    |