Home
Class 12
MATHS
If y=x^((x^(x))) then (dy)/(dx) is...

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

A

`y[x^(x)(log ex)log x+x^(x)]`

B

`y[x^(x)(log ex)log x+x]`

C

`y[x^(x)(log ex)log x+x^(-1)]`

D

`y[x^(x)(log_(e)x)log x+x^(-1)]`

Text Solution

AI Generated Solution

To find the derivative of the function \( y = x^{(x^x)} \), we will follow these steps: ### Step 1: Rewrite the function Let \( t = x^x \). Then, we can express \( y \) as: \[ y = x^t \] ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Linked Comprehension Type|24 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If y=x^(x^(2)), then (dy)/(dx) equals

If y=e^(x) then (dy)/(dx)

Let y = x^(x^(x...oo))," then " (dy)/(dx) is equal to

If y=x^(x) then Find (dy)/(dx)

If y=(x^(2))/((x+1))"then"(dy)/(dx)"is":-

If y={f(x)}^(phi(x)),"then"(dy)/(dx) is

If y=x^(sin x), then find (dy)/(dx)

If y = e^(-x) , then (dy)/(dx) is

If y= cos x^(@), then (dy)/(dx) is?

If y=(lnx)/(x) "then" (dy)/(dx) will be:

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. The first derivative of the function [cos^(-1)(sinsqrt((1+x)/(2)))+x^(...

    Text Solution

    |

  5. Let f(x)=x^(3),x in (0,oo) and let g(x) be inverse of f(x), then g'(x)...

    Text Solution

    |

  6. If y=ax^(n+1)+bx^(-n)," then "x^(2)(d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |

  7. If y=ax^(n+1)+bx^(-n)," then "x^(2)(d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |

  8. Suppose f(x)=e^(ax) + e^(bx), where a!=b, and that fprimeprime(x)-2fpr...

    Text Solution

    |

  9. (d^(20)y)/(dx^(20))(2cosxcos3x)is equal to 2^(20)(cos2x-2^(20)os3x) ...

    Text Solution

    |

  10. (d^n)/(dx^n)(logx)=? (a)((n-1)!)/(x^n) (b) (n !)/(x^n) (c)((n-2)!)/(...

    Text Solution

    |

  11. The n t h derivative of the function f(x)=1/(1-x^2)[w h e r ex in (-1,...

    Text Solution

    |

  12. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

    Text Solution

    |

  13. 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

    |

  14. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

    Text Solution

    |

  15. 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

    |

  16. A function f satisfies the condition f(x)=f^(prime)(x)+f''(x)+f'''(x)....

    Text Solution

    |

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

    Text Solution

    |

  18. If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...

    Text Solution

    |

  19. If y=x+e^x ,t h e n(d^(2x))/(dy^2)i s e^x (b) -(e^x)/((1+e^x)^3) -(e...

    Text Solution

    |

  20. if y= sin mx, them the value of the determinant |{:(y,,y(1),,y(...

    Text Solution

    |