Home
Class 12
MATHS
people living at Mars ,instead of the us...

people living at Mars ,instead of the usual definition of derivative `Df(x)` define a new kind of derivative `Df(x)` by the formula `Df(x)=lim_(h->0) (f^2(x+h)-f^2(x))/h` where `f^x` means `[f(x)]^2.` If `f(x)=xInx` then `Df(x)|_(x=e)` has the value (a) `e` (b) `2e` (c) `4e` (d) non

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

People living at Mars,instead of the usual definition of derivative Df(x) ,define a new kind of derivative D^(*)f(x) by the formula D^(*)f(x)=lim_(h rarr0)(f^(2)(x+h)-f^(2)(x))/(h) where f^(2)(x)means[f(x)]^(2) .If f(x)=x ln x then D^(*)f(x)|_(x=e) has the value (A)e(B)2e(C)4e(D) none

Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D^*F(x) by the formula D*f(x)=lim_(h->0)(f^2(x+h)-f^2(x))/h ,w h e r ef^2(x) mean [f(x)]^2 and if f(x)=xlogx ,then D^*f(x)|_(x=e) has the value (A)e (B) 2e (c) 4e (d) none of these

Instead of the usual defination of derivatie Df(x), if we define a new kind of derivatie D^(**)F(x) by the formula D^(**)(x)=lim_(hrarr0) (f^(2)(x+h)-f^(2)(x))/(h)." where "f^(2)(x)" means "[f(x)]^(2) and if f(x)=x log x, then D^(**)f(x)|_(x=e) has the value

Let the derivative of f(x) be defined as D*f(x)=lim_(h rarr0)(f^(2)(x+h)-f^(2)(x))/(h) where f^(2)(x)=(f(x))^(2) if u=f(x),v=g(x), then the value of D*{u.v} is

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

D*f(x)=lim_(h rarr0)(f^(2)(x+h)-f^(2)(x))/(h) If f(x)=x ln x then D*f(x) at x=e equals

Derivative of f(x) = 3^(x) is (ii) Derivative of f(x) = e^(2x) is

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

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

BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If y=a t^2+2b t+c&t=a x^2+2b x+c , then (d^3y)/(dx^3) equals 24 a^2(a ...

    Text Solution

    |

  2. Let f(x)=|cosxsinxcosxcos2xsin2x2cos2xcos3xsin3x3cos3x| then f'(pi/2)=...

    Text Solution

    |

  3. people living at Mars ,instead of the usual definition of derivative D...

    Text Solution

    |

  4. (lim)(xvec0^+)1/(xsqrt(x))("a t a n"^(-1)(sqrt(x))/a-btan^(-1)(sqrt(x)...

    Text Solution

    |

  5. Let y=ln(1+cosx)^2 then the value of (d^2y)/(dx^2)+2/(e^(y//2)) equals...

    Text Solution

    |

  6. If a curve is represented parametrically by the equation x=f(t) and y=...

    Text Solution

    |

  7. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  8. The derivative of the function, f(x)=cos^(-1){(1)/(sqrt13)(2cosx-3sin...

    Text Solution

    |

  9. Left hand derivative of sin^(- 1)((2x)/(1+x^2)) with respect to cos^-...

    Text Solution

    |

  10. If x^2+y^2=R^2(w h e r eR >0)a n dk=(y^n)/((1+y^2)^3) then find k in ...

    Text Solution

    |

  11. If y=1/(1+x^(n-m)+x^(p-m))+1/(1+x^(m-n)+x^(p-n))+1/(1+x^(m-p)+x^(n-p))...

    Text Solution

    |

  12. A curve is represented parametrically by the equations x = e^t cos t a...

    Text Solution

    |

  13. If F(t)=int(x+y)dt then the value of F(pi/2)-F(0) is 1 (b) -1 (...

    Text Solution

    |

  14. If 2^x+2^y=2^(x+y) then (dy)/(dx)

    Text Solution

    |

  15. Two functions f & g have first & second derivatives at x=0 & satisfy t...

    Text Solution

    |

  16. Let P(x) be the polynomial x^3+a x^2+b x+c , where a ,\ b ,\ c in R ....

    Text Solution

    |

  17. If sqrt(y+x)+sqrt(y-x)=c (where c!=0 ), then dy/dx

    Text Solution

    |

  18. For the function y=f(x)=(x^2+b x+c)e^x , which of the following holds?...

    Text Solution

    |

  19. Let f'(x)=3x^2sin1/x-xcos1/x , if x!=0\ ; f(0)=0 and f(1//pi)=0 then: ...

    Text Solution

    |

  20. If f(x)=xdot|x|, then its derivative is : (a)2x (b) -2x (c) 2|x|...

    Text Solution

    |