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Math Help - Whats an easy way to remember d/dx of b^x and logb^x

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    Whats an easy way to remember d/dx of b^x and logb^x

    Whats an easy way to remember  \frac{d}{dx}[b^x] and \frac{d}{dx} logb ^x besides remembering the d/dx formulas for them?

    I am in calc 2 and I forgot! We haven't used them yet, thankfully.
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    Re: Whats an easy way to remember d/dx of b^x and logb^x

    Quote Originally Posted by delgeezee View Post
    Whats an easy way to remember  \frac{d}{dx}[b^x] and \frac{d}{dx} logb ^x besides remembering the d/dx formulas for them?

    I am in calc 2 and I forgot! We haven't used them yet, thankfully.
    derive them yourself ...

    y = b^x

    \ln{y} = \ln{b^x}

    \ln{y} = x\ln{b}

    \frac{d}{dx} \left(\ln{y} = x\ln{b}\right)

    \frac{y'}{y} = \ln{b}

    y' = y \cdot \ln{b}

    y' = b^x \cdot \ln{b}

    ------------------------------------------------

    y = \log_b{x}

    x = b^y

    \frac{d}{dx}\left(x = b^y\right)

    1 = b^y \cdot \ln{b} \cdot y'

    1 = x \cdot \ln{b} \cdot y'

    y' = \frac{1}{x \cdot \ln{b}}
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