6: Derivatives of Products, Quotients, and Compositions
- Page ID
- 36872
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.
\[\begin{array}\
&\text{Primary Formulas}\\
&{\begin{array}\
{[C]^{\prime} } &=0 & {\left[t^{n}\right]^{\prime} } &=n t^{n-1} \\
{\left[e^{t}\right]^{\prime} } &=e^{t} & {[\ln t]^{\prime} } &=\frac{1}{t} \\
{[\sin t]^{\prime} } &=\cos t & {[\cos t]^{\prime} } &=-\sin t \\
\end{array}}\\
&\text{Combination Formulas}\\
&{\begin{array}\
{[u+v]^{\prime} } &=[u]^{\prime}+[v]^{\prime} & {[C u]^{\prime} } &=C[u]^{\prime} \\
{[u v]^{\prime} } &=[u]^{\prime} v+u[v]^{\prime} & {\left[\frac{u}{v}\right]^{\prime} } &=\frac{v[u]^{\prime}-u[v]^{\prime}}{u^{2}} \\
{[G(u)]^{\prime} } &=G^{\prime}(u) u^{\prime} & &
\end{array}}\\
\end{array}\]