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Math Help - Definition of a Derivative and Limits

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    Definition of a Derivative and Limits

    I at least need help getting started.

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    Re: Definition of a Derivative and Limits

    Quote Originally Posted by trevor22 View Post
    I at least need help getting started.

    For the first, use \displaystyle \begin{align*} \frac{dy}{dt} = \lim_{h \to 0}\frac{y(t + h) - y(t)}{h} \end{align*}

    For the second...

    \displaystyle \begin{align*} 3^x\lim_{h \to 0}\frac{3^h - 1}{h} &= \lim_{h \to 0}\frac{3^x\left(3^h - 1\right)}{h} \\ &= \lim_{h \to 0}\frac{3^x3^h - 3^x}{h} \\ &= \lim_{h \to 0}\frac{3^{x+h} - 3^x}{h} \end{align*}

    Is this in the form \displaystyle \begin{align*} \lim_{h \to 0}\frac{f(x+h) - f(x)}{h} \end{align*}? If so, what is \displaystyle \begin{align*} f(x) \end{align*}?
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