Home
Class 11
MATHS
If f(x)=|x|+|x-1| , write the value of d...

If `f(x)=|x|+|x-1|` , write the value of `d/(dx)(f(x))`.

Text Solution

Verified by Experts

`f(x)=|x|+|x-1|`
`f(x)={(x+x-1=2x-1,x>=1)`
`x+(-(x-1))=1,0 < x < 1`
`-2x+1, x< =0}`
thus,`d/(dx)(f(x))`.=`{2,x>=1`
`0,0 < x < 1`
`-2, x< =0}`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    RD SHARMA|Exercise Solved Examples And Exercises|267 Videos

  • ELLIPSE

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x+1, then write the value of (d)/(dx)(fof)(x)

If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the value of (d)/(dx)((g(x))/(g(g(x)))) at x = 4 equals

Let f(x)=x^(5)+2x^(3)+3x+4 then the value of 28(d)/(dx)(f^(-1)) at x=-2 is

Let f:R rarr R be a one-one onto differentiable function,such that f(2)=1 and f'(2)=3. The find the value of ((d)/(dx)(f^(-1)(x)))_(x=1)

If a function is invertible the graph of its inverse is the mirror image of the function in y=x. If f^(-1)(x) is the inverse function of f(x), then f(f^(-1)(x))=f^(-1)(f(x))=x . The value of (d)/(dx)(f^(-1)(x))" at " x = 9 " for "f(x)=x^(3)-2x^(-3)+10" is "(x gt 0)

if (d)/(dx)f(x)=g(x), find the value of int_(a)^(b)f(x)g(x)dx

If adifferentiabl e function f(x)=e^(x)+2x is given,then equal to (d)/(dx)(f^(-1)(x)) at x=f(ln3) is equal to

If f(x)=(x^(2))/(|x|)backslash write (d)/(dx)((x))

If f(x)=x+7, and g(x)=x-7, x in R" them find "d/(dx)(fog )(x).

The function f(x)=e^(x)+x, being differentiable and one-to-one,has a differentiable inverse f^(-1)(x) .The value of (d)/(dx)(f^(-1)) at the point f(log2) is (a) (1)/(1n2) (b) (1)/(3)( c) (1)/(4) (d) none of these

RD SHARMA-DERIVATIVES-Solved Examples And Exercises
  1. Write the value of d/(dx)(x \ |x|).

    Text Solution

    |

  2. Write the value of d/(dx){(x+|x|)|x|}dot

    Text Solution

    |

  3. If f(x)=|x|+|x-1| , write the value of d/(dx)(f(x)).

    Text Solution

    |

  4. Write the value of the derivative of f(x)=|x-1|+|x-3| \ at \ x = 2.

    Text Solution

    |

  5. If f(x)=(x^2)/(|x|), write d/(dx)(f(x))

    Text Solution

    |

  6. Write the value of d/(dx)(log|x|).

    Text Solution

    |

  7. If f(1)=1,f^(prime)(1)=2, then write the value of lim(x->1)(sqrt(f(x))...

    Text Solution

    |

  8. Write the derivative of f(x)=3 \ |2+x| at x=-3.

    Text Solution

    |

  9. If |x|<1 and y=1+x+x^2+x^3+... , then write the value of (dy)/(dx)dot

    Text Solution

    |

  10. Let f(x)=x-[x], x in RR, then f^(prime)(1/2) is a. 3/2 b. 1 c. 0 d. -1

    Text Solution

    |

  11. If f(x)=(x-4)/(2sqrt(x)), then f^(prime)(1) is a. 5/4 b. 4/5 c. 1 d. 0

    Text Solution

    |

  12. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+... , then (dy)/(dx)= a. y+1 b. y-...

    Text Solution

    |

  13. If f(x)=1-x+x^2-x^3+...-x^(99)+x^(100), then f^(prime)(1) equals a. 15...

    Text Solution

    |

  14. If y=(1+1/(x^2))/(1-1/(x^2)), then (dy)/(dx)= a. -(4x)/((x^2-1)^2) b. ...

    Text Solution

    |

  15. If y=sqrt(x)+1/(sqrt(x)), then (dy)/(dx) \ at \ x=1 is a. 1 b. 1/2 c....

    Text Solution

    |

  16. If f(x)=x^(100)+x^(99)+...+x+1, then f^(prime)(1) is equal to a. 5050...

    Text Solution

    |

  17. If f(x)=1+x+(x^2)/2+...+(x^(100))/(100), then f^(prime)(1) is equal to...

    Text Solution

    |

  18. if y=(sinx+cosx)/(sinx-cosx), then (dy)/(dx) at x=0 is equal to

    Text Solution

    |

  19. If y=(sin(x+9))/(cosx), then (dy)/(dx) at x = 0 is: a. cos9 b. sin9 c...

    Text Solution

    |

  20. If f(x) = (x^n-a^n)/(x-a), then f'(a) is a. 1 b. 1/2 c. 0 d. does not ...

    Text Solution

    |