Home
Class 11
MATHS
If x^(logy)=logx then find dy/dx....

If `x^(logy)=logx` then find `dy/dx`.

Text Solution

Verified by Experts

The correct Answer is:
`:. (dy)/(dx)=(y)/(x)(l-logx.logy)/(log_(x)^(2))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise-9(d)|15 Videos

  • DIFFERENTIATION

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise-9(b)|37 Videos

  • APPLICATION OF DERIVATIVES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise-10(h)|35 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISE -6(B)|21 Videos

Similar Questions

Explore conceptually related problems

If y=Tan^(-1)(logx) then find dy/dx .

If y^(x)=x^(siny) then find dy/dx .

If y = Tan^(-1)(log x) then find (dy)/(dx)

If y=x^(2)e^(x)sinx , then find dy/dx .

If y = log (cosh 2x) then find (dy)/(dx)

If y ^(x) + x ^(y) + x ^(x) = a ^(b) then find (dy)/(dx)

If y=e^(t)+cost,x=logt+sint then find dy/dx .

If y = sin^(-1)(cos x) then find (dy)/(dx)

If y=x^((logx)^log(logx)) , then (dy)/(dx) is

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIATION-Exercise-9(c )
  1. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) then prove that dy/dx=(sqrt(1-y^...

    Text Solution

    |

  2. If y=xsqrt(a^(2)+x^(2))+a^(2)log(x+sqrt(a^(2)+x^(2))), then show that ...

    Text Solution

    |

  3. If x^(logy)=logx then find dy/dx.

    Text Solution

    |

  4. If y = tan^(-1)((3x-x^(3))/(1-3x^(2))) + tan^(-1) ((4x-4x^(3))/(1-6x^(...

    Text Solution

    |

  5. If x^(y)=y^(x) then show that dy/dx=(y(xlogy-y))/(x(ylogx-x)).

    Text Solution

    |

  6. If x ^(3) + y ^(3) =3 axy then (dy)/(dx) =

    Text Solution

    |

  7. Find the derivative dy/dx of the function y=((1-2x)^(2//3)(1+3x)^(-3//...

    Text Solution

    |

  8. Find the derivative (dy)/(dx) of each of the following functions. y=...

    Text Solution

    |

  9. Find (dy)/(dx) for the function (using logarithms). y = ((a - x ) ^(...

    Text Solution

    |

  10. Find (dy)/(dx) for the function (using logarithms). y = (x ^(3) sqrt...

    Text Solution

    |

  11. Differentiate sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5))).

    Text Solution

    |

  12. Find the derivative of (sinx)^(log x)+x^(sinx).

    Text Solution

    |

  13. Find the derivatives of the following functions. x^(x^(x))

    Text Solution

    |

  14. Find the derivative of (ii) (sinx)^(x)+x^(sinx) w.r.to x.

    Text Solution

    |

  15. Find the derivatives of the following functions. x^(3)+(cotx)^(x)

    Text Solution

    |

  16. If x^(y) + y^(x) = a^(b) then prove that (dy)/(dx)=-[(yx^(y-1)+y^(x)L...

    Text Solution

    |

  17. If f(x) = sin^(-1) sqrt((x-beta)/(alpha-beta)), g(x) = tan^(-1) sqrt((...

    Text Solution

    |

  18. If f(x)=(a^(2)-b^(2))^(-1//2).cos^(-1)((acosx+b)/(a+bcosx)) a gt b gt ...

    Text Solution

    |

  19. Differentiate (x^(2)-5x+8)(x^(3)+7x+9) by Using product rule

    Text Solution

    |

  20. Differentiate (x^(2)-5x+8)(x^(3)+7x+9) by Using product rule

    Text Solution

    |