Home
Class 11
MATHS
If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy...

If `y=e^(sqrt(x))+e^(-sqrt(x))` , then `(dy)/(dx)` is equal to (a)`(e^(sqrt(x)))/(2sqrt(x))` (b) `(e^(sqrt(x))-e^(-sqrt(x)))/(2sqrtx)` (c)`1/(2sqrt(x))sqrt(y^2-4)` (d) `1/(2sqrt(x))sqrt(y^2+4)`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x)-1)/(sqrt(x)+1))

Evaluate: int(e^(sqrt(x))cos(e^(sqrt(x))))/(sqrt(x))dx

If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)) then (dy)/(dx) is equals to

Evaluate: int(e^(sqrt(x))sin(e^(sqrt(x))))/(sqrt(x))dx

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

int (dx)/(sqrt(1+sqrt(x)))=(4)/(3)(sqrt(x)-2)sqrt(1+sqrt(x))+c

If y = sqrt(x+sqrt(x+sqrt(x+* * * infty))) then (dy)/(dx)=

int (dx)/((a+sqrt(x))^((3)/(2)))=4sqrt(1+sqrt(x))+(4)/(sqrt(1+sqrt(x)))+c

int (dx)/(sqrt(2e^(x)-1))=2 sec^(-1)(sqrt(2)e^((x)/(2)))+c

The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)))dx is equal to (a)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^3)))+c (b)e^x(1/(sqrt(1+x^2))-x/(sqrt((1+x^2)^3)))+c (c)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^5)))+c (d)none of these

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Find ("lim")(xto2)(xf(2)-2f(x))/(x-2) if f(2)=4 and f′(2)=1

    Text Solution

    |

  2. If y=x^(x^(x^x...oo) , find (dy)/(dx)

    Text Solution

    |

  3. If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a)(e^(sqr...

    Text Solution

    |

  4. Differentiate sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5))) with respect to x

    Text Solution

    |

  5. If f(x)=|sinx-|cosx||, then the value of f^'(x) at x=(7pi)/6 is (a) ...

    Text Solution

    |

  6. If y=(tanx)^((tanx)^((tanx).... ∞) ,then find (dy)/(dx) at x=pi/4

    Text Solution

    |

  7. If graph of y=f(x) is symmetrical about the y-axis and that of y=g(x) ...

    Text Solution

    |

  8. Differentiate the function with respect to x using the first principle...

    Text Solution

    |

  9. If x=t^2,y=t^3,t h e n(d^2y)/(dx^2) is (a)3/2 (b) 3/(4t) (c) 3/(2t) (...

    Text Solution

    |

  10. Using the first principle, prove that: d/(dx)(f(x)g(x))=f(x)d/(dx)(g(x...

    Text Solution

    |

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

    Text Solution

    |

  12. If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot

    Text Solution

    |

  13. Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot Then f...

    Text Solution

    |

  14. If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

    Text Solution

    |

  15. A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+...

    Text Solution

    |

  16. If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi), then find (dy...

    Text Solution

    |

  17. If x=logp and y=1/p ,then (a)(d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2...

    Text Solution

    |

  18. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)...

    Text Solution

    |

  19. Let y=ln(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

    Text Solution

    |

  20. Find (dy)/(dx)"for"y=xsinxlogxdot

    Text Solution

    |