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Math Help - First Principle of Derivative and Power Rule

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    Question First Principle of Derivative and Power Rule

    using the first principle of differentiation, find the first derivatives of

    f(x) = 3/x2 and 1/(sqrt x)3

    - if using product rule i know, but if using first principle, my ans not the same. Please help me.
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    Re: First Principle of Derivative and Power Rule

    How far can you get? Do you know what you are trying to find the limit of?
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    Re: First Principle of Derivative and Power Rule

    Did you hear about this formula  \frac{dy}{dx} = lim_{h\rightarrow 0} \frac{f(x+h)−f(x)}{h}

    This is called differentiation from first principles, (or the delta method). It gives the instantaneous rate of change of y with respect to x,

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    Re: First Principle of Derivative and Power Rule

    Quote Originally Posted by choi105 View Post
    using the first principle of differentiation, find the first derivatives of

    f(x) = 3/x2 and 1/(sqrt x)3

    - if using product rule i know, but if using first principle, my ans not the same. Please help me.
    Both of these (I assume there are two) are really simple algebra.

    Can you simply \frac{\dfrac{3}{(x+h)^2}-\dfrac{3}{x^2}}{h}~?
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    Re: First Principle of Derivative and Power Rule

    Quote Originally Posted by Plato View Post
    Both of these (I assume there are two) are really simple algebra.

    Can you simply \frac{\dfrac{3}{(x+h)^2}-\dfrac{3}{x^2}}{h}~?
    Plato, congrats, you have got 700 thanks , a nice number... which I would quickly transform into a prime
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