Home
Class 12
MATHS
Let f(x) = e^(x), g(x) = sin^(-1) x and ...

Let `f(x) = e^(x), g(x) = sin^(-1) x` and h(x) = f(g(x)) then `(h^(')(x))/(h(x)) =`

A

`sin^(-1)x`

B

`1/(sqrt(1-x^(2))`

C

`1/(1-x^(2))`

D

`e^(sin^(-1)x)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|206 Videos
  • ELLIPSE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|172 Videos

Similar Questions

Explore conceptually related problems

If f(x) = In (x), g(x) = x^3 then f(g(ab)) = …

If f(x) = (2)/(x-3), g(x) = (x-3)/(x+4) and h (x) = (-2(2x + 1))/(x^(2) + x - 12) , then lim_(x rarr 3) [f(x) + g(x) + h(x)] is equal to :

Let f(x) = sqrt(x) and g(x) = x find (i) (f + g) x (ii) (fg) x

If f(x)=2 x^(2)+x+1 and g(x)=3 x+1 then f o g(2)

If g(x) = 1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) =

Let f(x) = |sin x|. Then

If g(f(x))=|sin x| and f(g(x))=(sin sqrt(x))^(2) then

HIMALAYA PUBLICATION-DIFFERENTIATION-QUESTION BANK
  1. If 2^(x)+2^(y)=2^(x+y), then (dy)/(dx) is

    Text Solution

    |

  2. If x = (2t)/(1+t^(2)), y = (1-t^(2))/(1+t^(2)) then dy/dx =

    Text Solution

    |

  3. Let f(x) = e^(x), g(x) = sin^(-1) x and h(x) = f(g(x)) then (h^(')(x))...

    Text Solution

    |

  4. If f(x)= sqrt(ax) + a^(2)/(sqrt(ax) then f^(')(a) =

    Text Solution

    |

  5. If f(x) {((x-1)/(2x^(2)-7x+5), x ne 1),(-1/3, x = 1):} then f^(')(1) =

    Text Solution

    |

  6. If f(x) = x/(1+|x|) for x in R, then f^(')(0) =

    Text Solution

    |

  7. y = sin^(-1)x, then (1-x^(2)) (d^(2)Y)/(dx) x^(2)) =

    Text Solution

    |

  8. The derivative of an odd function is :

    Text Solution

    |

  9. f(x) = 10 cos x + (13 + 2x) sin x, then f^('')(x) + f(x) =

    Text Solution

    |

  10. If f : R rarr R is an even function which is twice differentiable on R...

    Text Solution

    |

  11. If f(x)=sin^(-1)((2x)/(1+x^(2))), then f(sqrt3) is

    Text Solution

    |

  12. If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/...

    Text Solution

    |

  13. If x^(y) = y^(x) find (dy)/(dx)

    Text Solution

    |

  14. If sec ((x+y)/(x-y)) = a, then dy/dx =

    Text Solution

    |

  15. Derivative of f(x) = log(5)(log(7)x), where x gt 7 is

    Text Solution

    |

  16. If g is the inverse function of f and f^(')(x) = 1/(1+x^(n)), then g^(...

    Text Solution

    |

  17. If x = sin^(-1) (3t-4t^(3)) and y = cos^(-1) sqrt(1-t^(2)), and -1/2 l...

    Text Solution

    |

  18. If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)), then dy/dx ...

    Text Solution

    |

  19. If sqrt(1-x^(6)) + sqrt(1-y^(6)) = a^(3)(x^(3)-y^(3)) then dy/dx =

    Text Solution

    |

  20. If f(x) = (x^(2)-x)/(x^(2)+2x), then d/dx [f^(-1)(x)] =

    Text Solution

    |