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 \(\frac{dy}{dx}\) for the function \(y = (x^x)^x\), we can follow these steps: ### Step 1: Rewrite the function Start by rewriting the function: \[ y = (x^x)^x = x^{x^2} \] ...
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) then Find (dy)/(dx)

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

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

If x+y=sin(x+y) then (dy)/(dx)=

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

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

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

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

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

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

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)(sin sqrt((1+x)/2))+x^x]...

    Text Solution

    |

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

    Text Solution

    |

  6. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  7. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  8. Suppose f(x)=e^(ax)+e^(bx)," where " a ne b, and that f''(x) -2f'(x)-1...

    Text Solution

    |

  9. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a l to a)2^(20)(cos2x-2^(20)o...

    Text Solution

    |

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

    Text Solution

    |

  11. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

    Text Solution

    |

  12. 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

    |

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

    Text Solution

    |

  14. If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is

    Text Solution

    |

  15. A function f satisfies the condition f(x)=f'(x)+f''(x)+f'''(x)+…, wher...

    Text Solution

    |

  16. Let f(x) be a polynomial of degree 3 such that f(3)=1, f'(3)=-1, f''(3...

    Text Solution

    |

  17. 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

    |

  18. "If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=

    Text Solution

    |

  19. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

    Text Solution

    |

  20. Let y=ln (1+ cos x)^(2). The the value of (d^(2)y)/(dx^(2))+(2)/(e^(y/...

    Text Solution

    |