Home
Class 12
MATHS
If y=a^x^a^x^...^(((((oo))))) , then pr...

If `y=a^x^a^x^...^(((((oo)))))` , then prove that `(dy)/(dx)=(y^2(log)_e y)/(x(1-y(log)_e x(log)_e y)`

Promotional Banner

Topper's Solved these Questions

  • BOARD PAPER SOLUTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|65 Videos

  • DETERMINANTS

    RESONANCE DPP ENGLISH|Exercise All Questions|4 Videos

Similar Questions

Explore conceptually related problems

If y=a^(x^(a^x..oo)) then prove that dy/dx=(y^2 log y )/(x(1-y log x log y))

If y=x^x then prove that is (dy)/(dx)=x^(x)log_(e)(ex) .

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

If x=y log(xy) , then prove that (dy)/(dx) = (y (x-y))/(x(x+y)) .

Solve (dy)/(dx)+(y)/(x)=log x.

If y=(sin x) ^(sin x ^sin x ....oo) then prove that dy/dx=(y^2 cot x)/(1-y log (sin x))

If y=e^(x+e^(x+e^(x+dotto\ oo))) , show that (dy)/(dx)=y/(1-y) .

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

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

If x^(y) y^(x)=5 , then show that (dy)/(dx)= -(log y + (y)/(x))/(log x + (x)/(y))

RESONANCE DPP ENGLISH-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. about to only mathematics

    Text Solution

    |

  2. If the function f(x)=(x^2)/2+lnx+a x is always monotonically increasi...

    Text Solution

    |

  3. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)}...

    Text Solution

    |

  4. (d^2x)/(dy^2) equals: ((d^2y)/(dx^2))^(-1) (b) -((d^2y)/(dx^2))^(-1)(...

    Text Solution

    |

  5. y=tan^(-1)""(4x)/(1+5x^(2))+tan^(-1)""(2+3x)/(3-2x)

    Text Solution

    |

  6. If f (x) =lim (x to oo) x ((3)/(2) + [cos x)(sqrt(n^(2) +1)-sqrt(n ^(2...

    Text Solution

    |

  7. If g(x)=(2h(x)+|h(x)|)/(2h(x)-|h(x)|) where h(x)=sinx-sin^n x ,n in R...

    Text Solution

    |

  8. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

    Text Solution

    |

  9. If If {:(" ""x"),(y=""),(" ""x"),(" ""a+")...

    Text Solution

    |

  10. Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiatio...

    Text Solution

    |

  11. If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)e ...

    Text Solution

    |

  12. Let f(x)={s in2x ,0<xlt=pi//6a x+b ,pi//6<x<1 . If f(x)a n df^(prime)(...

    Text Solution

    |

  13. If f is twice differentiable such that f''(x)=-f(x), f'(x)=g(x), h'(x...

    Text Solution

    |

  14. Find (dy)/(dx) : x=a{cost+1/2logt a n^2t/2} and y=asint .

    Text Solution

    |

  15. If x^m y^n=(x+y)^(m+n), prove that (dy)/(dx)=y/x .

    Text Solution

    |

  16. If e^f(x)= log x and g(x) is the inverse function of f(x), then g'(x)...

    Text Solution

    |

  17. "If "y=sec (tan^(-1)x)," then "(dy)/(dx)" at "x=1 is equal to

    Text Solution

    |

  18. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

    Text Solution

    |

  19. If f(x)=2ln(x-2)-x^2+4x+1, then find the solution set of the inequalit...

    Text Solution

    |

  20. Differentiate the given functions w.r.t.x. (ln"x")^(cos"x")

    Text Solution

    |