Home
Class 12
MATHS
Find dy/dx if sec(x+y) = xy...

Find `dy/dx` if `sec(x+y) = xy`

Text Solution

Verified by Experts

The correct Answer is:
N/a
We have, `sec(x+y) = xy`
On differentiating both sides w.r.t. we get
` (d)/(dx) sec (x+y) = d/(dx) (xy)`
`rArr sec (x+y).tan(x+y).(d)/(dx)(x+y)=x.d/dx y+y.(d)/(dx) x`
`rArr sec(x+y). tan(x+y).(1+(dy)/(dx)) = x '(dy)(dx) + y`
`rArr sec(x+y)tan(x+y)+sec(x+y).tan(x+y).(dy)/(dx)=x'(dy)/(dx) + y`
`rArr (dy)/(dx) [sec (x+y).tan(x+y)-x] = y - sec(x+y).tan(x+y)`
`:. (dy)/(dx) = (y-sec(x+y).tan(x+y))/(sec(x+y).tan(x+y)-x)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR|Exercise Application Of Integrals|68 Videos

  • DETERMINANTS

    NCERT EXEMPLAR|Exercise Determinants|58 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) if xy - x = 1.

Find (dy)/(dx) if x^2+y^2=4xy

Find (dy)/(dx) , when: cot(xy)+xy=y

Find (dy)/(dx) , when If y = sqrt((sec x - tanx)/(sec x + tanx)) , show that (dy)/(dx) = sec x (tanx - sec x) .

NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. Differentiate tan^(-1)((sqrt(1+x^2-1))/x)wdotrdotttan^(-1)x ,w h e r e...

    Text Solution

    |

  2. If sin(x y)+y/x=x^2-y^2 , find (dy)/(dx) .

    Text Solution

    |

  3. Find dy/dx if sec(x+y) = xy

    Text Solution

    |

  4. Find (dy)/(dx) if, tan^(-1)(x^2+y^2)=a

    Text Solution

    |

  5. If (x^2+y^2)^2=x y , find (dy)/(dx)

    Text Solution

    |

  6. If a x^2+2\ h x y+b y^2+2\ gx+2\ fy+c=0 , find (dy)/(dx) and (dx)/(dy)...

    Text Solution

    |

  7. If x=e^(x//y) , prove that (dy)/(dx)=(x-y)/(xlogx)

    Text Solution

    |

  8. If y^x=e^(y-x) , prove that (dy)/(dx)=((1+logy)^2)/(logy)

    Text Solution

    |

  9. If y=(cosx)^(cosx)^(cosx)^^((((oo)))),p rov et h a t(dy)/(dx)=-(y^2tan...

    Text Solution

    |

  10. If sin(a+y)+sina.cos(a+y)=0. Prove that : (dy)/(dx)=(sin^2(a+y)/(sina...

    Text Solution

    |

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

    Text Solution

    |

  12. If y=tan^(-1)x , find (d^2y)/(dx^2) in terms of y alone.

    Text Solution

    |

  13. Verify Rolles theorem for function f(x)=x(x-1)^2 on [0,\ 1]

    Text Solution

    |

  14. Verify Rolles theorem for function f(x)=s in^4\ x+cos^4\ x on [0,\ ...

    Text Solution

    |

  15. Verify Rolles theorem for function f(x)=log(x^2+2)-log3 on [-1,\ 1]

    Text Solution

    |

  16. Verify Rolles theorem for the function: f(x)=x(x+3)e^(-x//2) on [-3...

    Text Solution

    |

  17. Verify Rolles theorem for the function f(x)=sqrt(4-x^2) on [-2,\ 2]...

    Text Solution

    |

  18. Discuss the applicability of Rolles theorem on the function f(x)={x...

    Text Solution

    |

  19. Using Rolle's theorem find the point in ( 0, 2 pi) on the curve y = co...

    Text Solution

    |

  20. Using Rolle's theroem, find the point on the curve y = x (x-4), x in ...

    Text Solution

    |