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6: Derivatives of Products, Quotients, and Compositions

  • Page ID
    36872
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    Where are we going?

    The basic derivative formulas that you need are shown below. Many additional derivative formulas are derived from them.

    The trigonometric derivatives are develop in Chapter 7. The last three Combination Rules are developed in this chapter.

    \[\begin{array}\

    &\text{Primary Formulas}\\

    &{\begin{array}\
    {[C]^{\prime} } &=0 & {\left[t^{n}\right]^{\prime} } &=n t^{n-1} \\
    {\left[e^{t}\right]^{\prime} } &=e^{t} & {[\ln t]^{\prime} } &=\frac{1}{t} \\
    {[\sin t]^{\prime} } &=\cos t & {[\cos t]^{\prime} } &=-\sin t \\
    \end{array}}\\

    &\text{Combination Formulas}\\

    &{\begin{array}\
    {[u+v]^{\prime} } &=[u]^{\prime}+[v]^{\prime} & {[C u]^{\prime} } &=C[u]^{\prime} \\
    {[u v]^{\prime} } &=[u]^{\prime} v+u[v]^{\prime} & {\left[\frac{u}{v}\right]^{\prime} } &=\frac{v[u]^{\prime}-u[v]^{\prime}}{u^{2}} \\
    {[G(u)]^{\prime} } &=G^{\prime}(u) u^{\prime} & &
    \end{array}}\\

    \end{array}\]

     


    This page titled 6: Derivatives of Products, Quotients, and Compositions is shared under a CC BY-NC-ND license and was authored, remixed, and/or curated by James L. Cornette & Ralph A. Ackerman.

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