Home
Class 12
MATHS
If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(...

If `f(0)=f(1)=0` , `f^(prime)(1)=f^(prime)(0)=2` and `y=f(e^x)e^(f(x))` , write the value of `(dy)/(dx)` at `x=0` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|logx|,xgt0 ,find f^(prime)(1/e)a n df^(prime)(e)

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2 and y(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If f(x)=(log)_e((log)_e x) , then write the value of f^(prime)(e) .

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0), then the value of k is

If f^(prime)(1)=2 and y=f((log)_e x) , find (dy)/(dx) at x=e .

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0), then the value of g^(prime)(1) is ________

Let y=f(x) satisfies (dy)/(dx)=(x+y)/(x) and f(e)=e then the value of f(1) is

If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

Let f(x) be differentiable for real x such that f^(prime)(x)>0on(-oo,-4), f^(prime)(x) 0on(6,oo), If g(x)=f(10-2x), then the value of g^(prime)(2) is a. 1 b. 2 c. 0 d. 4

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If pilt=xlt=2pi and y=cos^(-1)(cosx) , find (dy)/(dx) .

    Text Solution

    |

  2. Find dy/dx if x=sin^2y

    Text Solution

    |

  3. If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , wr...

    Text Solution

    |

  4. If y=x|x| , find (dy)/(dx) for x<0 .

    Text Solution

    |

  5. If y=sin^(-1)x+cos^(-1)x ,\ find (dy)/(dx) .

    Text Solution

    |

  6. If x=a(theta+sintheta),\ \ y=a(1+costheta) , find (dy)/(dx) .

    Text Solution

    |

  7. If y=x^x , find (dy)/(dx) at x=e .

    Text Solution

    |

  8. If y=tan^(-1)((1-x)/(1+x)) , find (dy)/(dx) .

    Text Solution

    |

  9. If y=(log)a x , find (dy)/(dx) .

    Text Solution

    |

  10. If y=logsqrt(tanx) , write (dy)/(dx) .

    Text Solution

    |

  11. If y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , find (dy)/(...

    Text Solution

    |

  12. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

    Text Solution

    |

  13. If |x|<1 and y=1+x+x^2+\ ddotto\ oo , then find the value of (dy)/(...

    Text Solution

    |

  14. If u=sin^(-1)((2x)/(1+x^2)) and v=tan^(-1)((2x)/(1-x^2)) , where -1<x<...

    Text Solution

    |

  15. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

    Text Solution

    |

  16. If y=log(3x),\ \ x!=0 , find (dy)/(dx) .

    Text Solution

    |

  17. If f(x) is an even function, then write whether f^(prime)(x) is eve...

    Text Solution

    |

  18. If f(x) is an odd function, then write whether f^(prime)(x) is even...

    Text Solution

    |

  19. Write the derivative of sinx w.r.t. cosxdot

    Text Solution

    |

  20. If f(x)=(log)(x^2)(logx) , then f^(prime)(x) at x=e is (a) 0 (b) 1 (c)...

    Text Solution

    |