Home
Class 11
MATHS
If y=1=x/(1!)+(x^2)/(2!)+(x^3)/(3!)+ , s...

If `y=1=x/(1!)+(x^2)/(2!)+(x^3)/(3!)+ ,` show that `(dy)/(dx)=ydot`

Text Solution

Verified by Experts

We have , `y = e^(x)`.
`:. (dy)/(dx) = d/(dx) (e^(x)) = y`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exrescise 28A|13 Videos

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exrescise 28B|21 Videos

  • DIFFERENTIATION

    RS AGGARWAL|Exercise Exercise 28E|44 Videos

  • CONDITIONAL IDENTITIES INVOLVING THE ANGLES OF A TRIANGLE

    RS AGGARWAL|Exercise EXERCISE 16|12 Videos

  • ELLIPSE

    RS AGGARWAL|Exercise EXERCISE|26 Videos

Similar Questions

Explore conceptually related problems

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

If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)+, is (dy)/(dx)=y+1 b.y-1 c.y d.y^(2)

If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)++(x^(n))/(n!), show that (dy)/(dx)-y+(x^(n))/(n!)=0

If tan^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=a , show that (dy)/(dx)=(x(1-tana))/(y(1+tana)).

If y = (1)/( (x^(2) +3)) , then (dy)/(dx) =

If log _(10)((x^(3)-y^(3))/(x^(3)+y^(3))) = 2 , then show that (dy)/(dx) = (-99x^(2))/(101y^(2))

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

If y={(1-tan x)/(1+tan x)}, show that (dy)/(dx)=(-2)/(1+sin2x)

if x=(1+ln t)/(t^(2)) and y=(3+2ln t)/(t) then show that y(dy)/(dx)=2x((dy)/(dx))^(2)+1

If y=3x^(3)sin^(-1)x+(x^(2)+2)sqrt(1-x^(2)), then (dy)/(dx)=

RS AGGARWAL-DIFFERENTIATION-Solved Examples
  1. Differentiate the following function : (i) (x^(2) - 5x + 6)(x-3) , (...

    Text Solution

    |

  2. If y=sqrt((1-cos2x)/(1+cos2x)), where 0 < x < pi/2, find (dy)/(dx).

    Text Solution

    |

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

    Text Solution

    |

  4. If u = 3t^(4) - 5t^(3) + 2t^(2) - 18t+4, find (du)/(dt) at t = 1.

    Text Solution

    |

  5. Differentiate x^(6) from the first principle.

    Text Solution

    |

  6. Differentiate each of the following from first principle: e^(3x)

    Text Solution

    |

  7. Find the derivative of each of the following from the first principle....

    Text Solution

    |

  8. Differentiate each of the following (i) (x+5)^(7) , (ii) (x-1/x)

    Text Solution

    |

  9. Find the derivative of each of the following from the first principle....

    Text Solution

    |

  10. Differentiate each of the following from first principle: xsinx

    Text Solution

    |

  11. Differentiate (sinx)/(x) from the first principle .

    Text Solution

    |

  12. Differentiate cot (2x+1) from the first principle.

    Text Solution

    |

  13. Find the derivative of each of the following from the first principle ...

    Text Solution

    |

  14. Find the derivative of x^(-3//2) from the first principle .

    Text Solution

    |

  15. Find the derivative of (1)/(x^(2)) from the first principle .

    Text Solution

    |

  16. Differentiate sqrt(sin3x) from the first principle.

    Text Solution

    |

  17. Find the derivative of e^(sqrt(x)) from the first principle.

    Text Solution

    |

  18. Find the derivative of e^(x^(2)) from the first principle.

    Text Solution

    |

  19. Find the derivative of e^(sinx ) from the first principle.

    Text Solution

    |

  20. Differentiate each of the following from the first principle. (i) sq...

    Text Solution

    |