Home
Class 12
MATHS
If f(x) = 3^(x) " and" g(x) = 4^(x) , ...

If ` f(x) = 3^(x) " and" g(x) = 4^(x) , " then" (f'(0) - g'(0))/(1 +f'(0) g'(0)) ` is

A

`(log ""(3)/(4))/(1 + (log 3)(log 4)) `

B

`(log ""(3)/(4))/(1 + log 12)`

C

`(log 12)/(1 + log _(12))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Now `f'(x) = 3^(x) log 3 " and " g'(x) = 4^(x) log 4 `
` therefore f'(0) = 3^(@) " and" g' (0) = 4^(@) log 4 `
` rArr f'(0) = log 3 " and " g'(0) = log 4 `
`therefore (f'(0) -g'(0))/(1 + f'(0) g'(0)) = (log 3 - log 4)/(1 + log 3 log 4) = (log"" (3)/(4))/(1 + log 3 log 4)` .
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

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

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 1 (HIGHER ORDER DERIVATIVE )|15 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

If f(x)=3x+1 and g(x)=x^(3)+2 then ((f+g)/(f*g))(0) is:

Let f(x)=e^(x)g(x),g(0)=4 and g'(0)=2, then f'(0) equals

If f(x)=1+cos x and g(x)=(a)/(bx^(2)+cx+1) If (0)=g(0),f'(0)=g'(0),f''(0)=g''(0) and the area bounded by the graph of g(x) and x-axis is k pi then find the value of k.

If f(x)=sin x and g(x)=f(f(f,.....(f(x)))) then value of g'(0)+g''(0)+g'''(0) equals

If f(x)=e^xg(x), g(0)=2, g'(0)=1 , then f'(0) is equal to.......

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. If y = tan^(-1) (x)/(2) - cot ^(-1) (x)/(2) , "then" (dy)/(dx) is eq...

    Text Solution

    |

  2. If y = ((x^(a))/(x^(b)))^(a + b) ((x^(b))/(x^(c)))^(b + c) ((x^(c))/(x...

    Text Solution

    |

  3. If f(x) = 3^(x) " and" g(x) = 4^(x) , " then" (f'(0) - g'(0))/(1 +f'...

    Text Solution

    |

  4. If y = sqrt((1+ sin x)/(1+ cos x)), " then" (dy)/(dx) is equal to

    Text Solution

    |

  5. If y = tan^(-1) ((4sqrt(x))/(1 - 4x))" then" (dy)/(dx) is

    Text Solution

    |

  6. If y = tan^(-1) ((4sqrt(x))/(1 - 4x))" then" (dy)/(dx) is

    Text Solution

    |

  7. (d)/(dx) "" tan^(-1) ((2e^(x))/(1 - e^(2x)))=

    Text Solution

    |

  8. If y = tan^(-1)((sin 3x - cos 3x )/(sin 3x + cos 3x))" then" (dy)/(dx...

    Text Solution

    |

  9. If y = loga x + log xa + log x x + logaa, thendy/dx is equal to

    Text Solution

    |

  10. If x = e^(x//y), then dy/dx is equal to

    Text Solution

    |

  11. If f(x) = log ((m(x))/(n(x))), m(1) = n(1) = 1 and m'(1) = n'(1)...

    Text Solution

    |

  12. If y = t^(2) + t - 1 " then " (dy)/(dx) is equal to

    Text Solution

    |

  13. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

    Text Solution

    |

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

    Text Solution

    |

  15. Let y=e^(2x)dotT h e n((d^2y)/(dx^2))((d^2x)/(dy^2))i s

    Text Solution

    |

  16. If f(x)=|x-2| and g(x)=f(f(x)), then g'(x)"for "x gt 20,is

    Text Solution

    |

  17. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

    Text Solution

    |

  18. The value of (d)/(dx) (|x-1| + |x -5|) at x = 3 is

    Text Solution

    |

  19. If y=f(x)" and "ycosx+cosy=pi, then the value of f''(0) is

    Text Solution

    |

  20. Derivatives of y = cos^(-1) sqrt((cos 3x)/(cos ^(3) x)) with respect ...

    Text Solution

    |