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28 August, 18:27

Find from first principles the derivative of x squared plus 2x

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  1. 28 August, 19:23
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    +Answer:

    The derivative is 2x + 2.

    Step-by-step explanation:

    The definition of the derivative is the limit of

    [ f (x + h) ^2 - f (x) ] / h when h - --> 0.

    For f (x) = x^2 + 2x:

    Derivative = the limit as h - -> 0 of f (x)

    = [ (x + h) ^2 + 2 (x + h) - (x^2 + 2x) ] / h

    = [x^2 + 2hx + h^2 + 2x + 2h - x^2 - 2x] / h

    = (2hx + 2h + h^2) / h

    = 2x + 2 + h

    The h can be neglected

    So it is 2x + 2.
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