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Section 5 Mathematical Formulas5-2 Differential and Integral Calcalus Formula 5-2-2 Differential Basic Formula 1.Differential Linearity \begin{eqnarray} \{af(x)+bg(x)\}'&=&af'(x)+bg'(x) \nonumber \end{eqnarray} 2.Differential of Product of Function \begin{eqnarray} \{f(x)g(x)\}'&=&f'(x)g(x)+f(x)g'(x) \nonumber \end{eqnarray} 3.Differential of Quotient of Function \begin{eqnarray} \{\frac{f(x)}{g(x)}\}'&=&\frac{f'(x)g(x)-f(x)g'(x)}{\{g(x)\}^2} \nonumber \end{eqnarray} 4.Differential of Composition Function \begin{eqnarray} \frac{dz}{dx}&=&\frac{dz}{dy}\frac{dy}{dx} \nonumber \end{eqnarray} 5.Differential of Inverse Function \begin{eqnarray} \frac{dy}{dx}&=&\frac{1}{dx/dy} \nonumber \end{eqnarray} 6.Differential by substitution \begin{eqnarray} \frac{dy}{dx}&=&\frac{dy/dt}{dx/dt}=\frac{g'(t)}{f'(t)}\;\;\;\;\;x=f(t),y=g(t) \nonumber \end{eqnarray} |