Home
Class 12
MATHS
The derivative of f(x) = e^(e^(x^(2))) i...

The derivative of `f(x) = e^(e^(x^(2))) `is

A

`2x e^(x^(2))`

B

` e^(e^(x^(2))) e^(x^(2))`

C

`2x e^(e^(x^(2))) e^(x^(2))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Given , ` y= e^(e^(x^(2)))`
On differentiating both sides w.r.t.x, we get
`(dy)/(dx)= e^(e^(x^(2)))(d)/(dx) (e^(x^(2))) = e^(e^(x^(2))) xxe^(x^(2))(d)/(dx) (x^(2)) = e^(e^(x^(2))) xxe^(x^(2))xx 2x `
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 1 DERIVATIVE OF INVERSE TRIGONOMETRIC FUNCTIONS (BY SUBSTITUTION)|18 Videos

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 1 ( DERIVATIVE OF FUNCTION WITH RESPECT TO ANOTHER FUNCTION )|10 Videos

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORER|35 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

Similar Questions

Explore conceptually related problems

The derivative of f(x) = (x^(4))/(e^(x)) is

The derivative of f(x) = x^(4) e^(x) is

The derivative of f(x)=e^(2x) is

"Find the derivative of "f(x)=e^(x)(x^(2)+1)

Derivative of f(x) = x + e^(x) is

Find the derivative of f(x)=a^(x)*e^(x^(2)

The derivative of x^(e^(x)) is

The derivative of f(x)=int_(x^(2))^(x^(3))(1)/(log_(e)(t))dt,(x>0), is

The anti - derivative of f(x) = e^(x//2) whose graph passes through the point (0,3) is :

The second order derivative of (e^(x)+1)/(e^(x)) is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF COMPOSITE FUNCTION (BY CHAIN RULE )
  1. If y = log ((cos x)/(1 - sin x)), "then " (dy)/(dx) is equal to

    Text Solution

    |

  2. If y= log (sqrt(x - 1)) - sqrt(x + 1)) ,"then " (dy)/(dx) is equal t...

    Text Solution

    |

  3. The derivative of f(x) = e^(e^(x^(2))) is

    Text Solution

    |

  4. If y= log [x + sqrt(9 + x^(2))], "then" (dy)/(dx) is equal to

    Text Solution

    |

  5. If y =sqrt(x) + (1)/(sqrt(x)) , "then" 2 x . (dy)/(dx) is equal to

    Text Solution

    |

  6. Derivative of 2sqrt(cot(x^(2))) with respect to x is

    Text Solution

    |

  7. Derivative of sqrt( tan sqrt(x)) with respect to x is

    Text Solution

    |

  8. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is

    Text Solution

    |

  9. If y = sqrt(sin + y ) "then" (dy)/(dx) is equal to

    Text Solution

    |

  10. The differential coefficient of sin (cos (x^(2))) with respect to s i...

    Text Solution

    |

  11. If y=sqrt(x(log)e x) , then find (dy)/(dx) at x=e .

    Text Solution

    |

  12. If y= ( cos x ^(2))^(2) , "then" (dy)/(dx) is equal to

    Text Solution

    |

  13. If y=cos(sinx^2) then at x=sqrt(pi/2), (dy)/(dx)=

    Text Solution

    |

  14. Derivative of log[log(log x^(5))] with respect to x is

    Text Solution

    |

  15. If f(x) = log(x^(2)) (log(e) x) "then f' (x) at x= e" is

    Text Solution

    |

  16. If y = log(2) log(2) (x) , " then " (dy)/(dx) is equal to

    Text Solution

    |

  17. If x=(1-sqrt(y))/(1+sqrt(y)) then (dy)/(dx) is equal to

    Text Solution

    |

  18. If y = log (sin (x^(2))), 0 lt x lt (pi)/(2), "then " (dy)/(dx) "at ...

    Text Solution

    |

  19. (d)/(dx)[log(e)e^(sin(x^(2)))] is equal to

    Text Solution

    |

  20. If y=sqrt((1-x)/(1+x)), then (1-x^(2))(dy)/(dx)+y is equal to

    Text Solution

    |