Resumen de fórmulas (derivadas)

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En las siguientes fórmulas de derivadas:
– u y v representan funciones
– a es una constante (un número)

Operaciones

\begin{tabular}{|c|} \hline [u+v]\textsc{\char13} = u\textsc{\char13}+v\textsc{\char13} \\ \hline [a\cdot u]\textsc{\char13} =a \cdot u\textsc{\char13} \\ \hline [u \cdot v]\textsc{\char13} = u\textsc{\char13}\cdot v + u\cdot v\textsc{\char13} \\ \hline \left[ \frac{u}{v} \right]\textsc{\char13} = \frac{u\textsc{\char13}\cdot v - u\cdot v\textsc{\char13}}{v^2} \\ \hline \end{tablar}

Fórmulas

\fbox{y=a \longrightarrow y\textsc{\char13}=0}

\fbox{y=x \longrightarrow y\textsc{\char13}=1}

\fbox{y=a\cdot x \longrightarrow y\textsc{\char13}=a}

\fbox{y= x^n \longrightarrow y\textsc{\char13}=nx^{n-1}}
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\fbox{y= u^n \longrightarrow y\textsc{\char13}=n \cdot u^{n-1}\cdot u\textsc{\char13}}

\fbox{y= e^x \longrightarrow y\textsc{\char13}=e^x}
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\fbox{y= e^{u} \longrightarrow y\textsc{\char13}=e^{u} \cdot u\textsc{\char13}}

\fbox{y= a^x \longrightarrow y\textsc{\char13}=a^x \cdot Ln(a)}
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\fbox{y= a^{u} \longrightarrow y\textsc{\char13}=a^{u} \cdot u\textsc{\char13} \cdot Ln(a)}

\fbox{y=Ln(x) \longrightarrow y\textsc{\char13}=\frac{1}{x}}
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\fbox{y=Ln(u) \longrightarrow y\textsc{\char13}=\frac{u\textsc{\char13}}{u}}

\fbox{y=sen(x) \longrightarrow y\textsc{\char13}=cos(x)}
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\fbox{y=sen(u) \longrightarrow y\textsc{\char13}=cos(u) \cdot u\textsc{\char13}}

\fbox{y=cos(x) \longrightarrow y\textsc{\char13}=-sen(x)}
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\fbox{y=cos(u) \longrightarrow y\textsc{\char13}=-sen(u) \cdot u\textsc{\char13}}

\fbox{y=tg(x) \longrightarrow y\textsc{\char13}=\frac{1}{cos^2(x)}=1+tg^2(x)}
\fbox{y=tg(u) \longrightarrow y\textsc{\char13}=\frac{u\textsc{\char13}}{cos^2(u)}=1+tg^2(u) \cdot u\textsc{\char13} }