Home
Class 11
MATHS
If y=sqrt(x)+1/(sqrt(x)), then (dy)/(dx)...

If `y=sqrt(x)+1/(sqrt(x))`, then `(dy)/(dx) \ at \ x=1` is a. 1 b. `1/2` c. `1/(sqrt(2))` d. 0

Text Solution

Verified by Experts

We have, `y=sqrt(x)+1/(sqrt(x))`
On taking differentiating both sides w.r.t x, we get
`(dy/dx)​=1/(2sqrt(x)) ...
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 y= sqrt(x-1) +sqrt( x+1) ,then (dy)/(dx)

If y=xsin^(-1)x+sqrt(1-x^2) then (dy)/(dx)=

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

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

If x sqrt(y+1)+y sqrt(x+1)=0 & x!=y, then (dy)/(dx)=

If y=sqrt(x)+(1)/sqrt(x) , then show that 2x(dy)/(dx)+y=2sqrt(x) .

If y=sqrt(x+1)+sqrt(x-1)," then: "2sqrt(x^(2)-1)*(dy)/(dx)=

If sqrt(x) + sqrt(y) = sqrt(a) , then (dy)/(dx) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt(a))

If y=log(sqrt(x)+(1)/(sqrt(x))), prove that (dy)/(dx)=(x-1)/(2x(x+1))

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. 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

    |

  20. If f(x) = xsinx, then f'(pi/2) is a. 1/2 b. 1 c. 0 d. -1

    Text Solution

    |