Home
Class 12
MATHS
If x^(p)y^(q)=(x+y)^(p+q), show that dy/...

If `x^(p)y^(q)=(x+y)^(p+q)`, show that `dy/dx=y/x`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(j) (LONG ANSWER TYPE QUESTIONS (I))|10 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(k) (SHORT ANSWER TYPE QUESTIONS)|19 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(i) (SHORT ANSWER TYPE QUESTIONS)|27 Videos
  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos
  • DETERMINANTS

    MODERN PUBLICATION|Exercise Chapter test 4|12 Videos

Similar Questions

Explore conceptually related problems

x^(p)*y^(q) = (x+y)^(p+q) prove that dy/dx= y/x

If x^(p)y^(q)=(x+y)^(p+q) , prove that (dy)/(dx)=(y)/(x)

If x^(p) + y^(q) = (x + y)^(p+q) , " then" (dy)/(dx) is

If x^(p) y^(q) = (x + y)^((p + q)) " then " (dy)/(dx)= ?

If x^py^q=(x+y)^(p+q) , then dy/dx= (a) x/y (b) y/x (c) x/(x+y) (d) y/(y+x)

(2) If a=x^(q+r)*y^(p) , b=x^(r+p)*y^(q) , c=x^(p+q)y^(r) , show that a^(q-r)b^(r-p)c^(p-q)=1

If x^py^q=(x+y)^(p+q) then the value of (d^(2)y)/(dx^(2)) is (where p,q in N ) (A) 0 (B) -1 (C) 1(D) None of these

If (x+iy)(p+iq)=(x^(2)+y^(2))i, prove that x=q,y=p

If (log x)/(q-r)=(log y)/(r-p)=(log z)/(p-q) prove that x^(q+r)*y^(r+p)*z^(p+q)=x^(p)*y^(q).z^(r)

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(i) (LONG ANSWER TYPE QUESTIONS (I))
  1. Differentiate the following w.r.t. x : x^(2)e^(x)sinx

    Text Solution

    |

  2. Differentiate the following w.r.t. x : e^(x)cos^(3)xsin^(2)x

    Text Solution

    |

  3. Differentiate the following w.r.t. x : (x+3)^(2)(x+4)^(3)(x+5)^(4)

    Text Solution

    |

  4. Differentiate the following w.r.t. x : sqrt((x-1)(x-2)(x-3)(x-4))

    Text Solution

    |

  5. If x y=e^(x-y) , find (dy)/(dx) .

    Text Solution

    |

  6. If (sinx)^(y)=(siny)^(x),"find "dy/dx.

    Text Solution

    |

  7. Find dy/dx" if "(sinx)^(cosy)=(cosy)^(sinx).

    Text Solution

    |

  8. Differentiate log(x^(x)+cosec^(2)x) w.r.t. x.

    Text Solution

    |

  9. If x^(p)y^(q)=(x+y)^(p+q), show that dy/dx=y/x.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. If x^x+y^x=1 , prove that (dy)/(dx)=-{(x^x(1+logx)+y^x logy)/(x y^((x...

    Text Solution

    |

  13. If x^(y)+y^(x)=1,"find "dy/dx

    Text Solution

    |

  14. If x^y+y^x=a^b , then find dy/dx.

    Text Solution

    |

  15. If x^(y)+y^(x)=4,"find "dy/dx

    Text Solution

    |

  16. If x^(y)+y^(x)=loga,"find "dy/dx.

    Text Solution

    |

  17. Show that if x^(y)+y^(x)=m^(n), then : dy/dx=-(y^(x)logy+yx^(y-1))/(...

    Text Solution

    |

  18. Find the derivative of the function given by : f(x)=(1+x)(1+x^(2))(1...

    Text Solution

    |

  19. Differentiate (x^2-5x+8)(x^3+7x+9) in three ways mentioned below:(i) ...

    Text Solution

    |

  20. If u, v and w are functions of x, then show thatd/(dx)(udotvdotw)=(d u...

    Text Solution

    |