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Jhannybean

  • 2 years ago

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  1. Jhannybean
    • 2 years ago
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    \begin{align} y &=\left(\dfrac{1+e^x}{1-e^x}\right)^{1/2} \\ \ln y &=\dfrac{1}{2}\ln \left(\dfrac{1+e^x}{1-e^x}\right) \\ \end{align}

  2. Jhannybean
    • 2 years ago
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    \begin{align} y &=\large{\left(\dfrac{1+e^x}{1-e^x}\right)^{1/2}} \\ \ln y &=\large{\dfrac{1}{2}\ln \left(\dfrac{1+e^x}{1-e^x}\right)} \\ \cfrac{d}{dx}(\ln y) &= \end{align}

  3. Jhannybean
    • 2 years ago
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    \begin{align} y &=\large{\left(\dfrac{1+e^x}{1-e^x}\right)^{1/2}} \\ \ln y &=\large{\dfrac{1}{2}\ln \left(\dfrac{1+e^x}{1-e^x}\right)} \\ \cfrac{d}{dx}(\ln y) &=\cfrac{1}{2}\cfrac{d}{dx}[\ln(1+e^x)-\ln(1-e^x)] \end{align}

  4. Jhannybean
    • 2 years ago
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    \begin{align} \large y &=\large{\left(\dfrac{1+e^x}{1-e^x}\right)^{1/2}} \\ \large \ln y &=\large{\dfrac{1}{2}\ln \left(\dfrac{1+e^x}{1-e^x}\right)} \\ \large \cfrac{d}{dx}(\ln y) &=\large \cfrac{1}{2} \cdot \cfrac{d}{dx}[\ln(1+e^x)-\ln(1-e^x)] \\ \large \dfrac{y'}{y} &= \large \cfrac{e^x}{2(1+e^x)}+\cfrac{e^x}{2(1-e^x)} \\ \end{align}

  5. Jhannybean
    • 2 years ago
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    \begin{align} \large y &=\large{\left(\dfrac{1+e^x}{1-e^x}\right)^{1/2}} \\ \large \ln y &=\large{\dfrac{1}{2}\ln \left(\dfrac{1+e^x}{1-e^x}\right)} \\ \large \cfrac{d}{dx}(\ln y) &=\large \cfrac{1}{2} \cdot \cfrac{d}{dx}[\ln(1+e^x)-\ln(1-e^x)] \\ \large \dfrac{y'}{y} &= \large \cfrac{e^x}{2(1+e^x)}+\cfrac{e^x}{2(1-e^x)} \\ \large \dfrac{y'}{y} &= \large \cfrac{e^x}{(1-e^x)^2} \\ \large y' &= \large y \cdot \cfrac{e^x}{(1-e^x)^2} \\ \large y' &= \large \left(\cfrac{1+e^x}{1-e^x}\right)^{1/2} \cdot \cfrac{e^x}{(1-e^x)^2} \\ \end{align}

  6. Machida
    • 2 years ago
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    ★░░░░░░░░░░░████░░░░░░░░░░░░░░░░░░░░★ ★░░░░░░░░░███░██░░░░░░░░░░░░░░░░░░░░★ ★░░░░░░░░░██░░░█░░░░░░░░░░░░░░░░░░░░★ ★░░░░░░░░░██░░░██░░░░░░░░░░░░░░░░░░░★ ★░░░░░░░░░░██░░░███░░░░░░░░░░░░░░░░░★ ★░░░░░░░░░░░██░░░░██░░░░░░░░░░░░░░░░★ ★░░░░░░░░░░░██░░░░░███░░░░░░░░░░░░░░★ ★░░░░░░░░░░░░██░░░░░░██░░░░░░░░░░░░░★ ★░░░░░░░███████░░░░░░░██░░░░░░░░░░░░★ ★░░░░█████░░░░░░░░░░░░░░███░██░░░░░░★ ★░░░██░░░░░████░░░░░░░░░░██████░░░░░★ ★░░░██░░████░░███░░░░░░░░░░░░░██░░░░★ ★░░░██░░░░░░░░███░░░░░░░░░░░░░██░░░░★ ★░░░░██████████░███░░░░░░░░░░░██░░░░★ ★░░░░██░░░░░░░░████░░░░░░░░░░░██░░░░★ ★░░░░███████████░░██░░░░░░░░░░██░░░░★ ★░░░░░░██░░░░░░░████░░░░░██████░░░░░★ ★░░░░░░██████████░██░░░░███░██░░░░░░★ ★░░░░░░░░░██░░░░░████░███░░░░░░░░░░░★ ★░░░░░░░░░█████████████░░░░░░░░░░░░░★ ★░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░★

  7. Jhannybean
    • 2 years ago
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    Medals 3

    \begin{align} \large \sqrt{s ^{8}} + \sqrt{25s ^{8}} + 2\sqrt{s ^{8}} - \sqrt{s ^{4}} &= \large s^{8/2} +(25^{1/2})(s^{8/2}) +2(s^{8/2})-s^{4/2} \\ &= \large s^4 +(5)(s^4)+2(s^4)-s^2 \\ \end{align}

  8. Jhannybean
    • 2 years ago
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    \begin{align} \large \cfrac{7x^2+11x-6}{7x^2 -10x+3} &= \large \cfrac{x^2 +11x -42}{x^2 -10x +21} \\ &= \large \cfrac{(x-14)(x+3)}{((x-7)(x-3)} \\ &= \large \cfrac{(x-\cfrac{14}{7})(x+\cfrac{3}{7})}{(x-\cfrac{7}{7})(x-\cfrac{3}{7})} \\ &= \large \cfrac{(x-2)(7x+3)}{(x-1)(7x-3)} \\ \end{align}

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