# General Theorems of Differentiation

• $\frac{{{\text{dy}}}}{{{\text{dx}}}}\left( {\text{c}} \right) = 0$
• $\frac{{\text{d}}}{{{\text{dx}}}}\left( {{{\text{x}}^{\text{n}}}} \right) = {\text{n}}{{\text{x}}^{{\text{n – 1}}}}$
• $\frac{{\text{d}}}{{{\text{dx}}}}\left[ {{\text{c}}f\left( {\text{x}} \right)} \right] = {\text{c}}f’\left( {\text{x}} \right)$
• $\frac{{{\text{dy}}}}{{{\text{dx}}}}\left[ {f\left( {\text{x}} \right) + g\left( {\text{x}} \right)} \right] = f’\left( {\text{x}} \right) + g’\left( {\text{x}} \right)$
• $\frac{{{\text{dy}}}}{{{\text{dx}}}}\left[ {f\left( {\text{x}} \right) – g\left( {\text{x}} \right)} \right] = f’\left( {\text{x}} \right) – g’\left( {\text{x}} \right)$
• $\frac{{\text{d}}}{{{\text{dx}}}}{\text{ = }}\left[ {f\left( {\text{x}} \right)g\left( {\text{x}} \right)} \right]{\text{ = }}f\left( {\text{x}} \right)g’\left( {\text{x}} \right){\text{ + }}g\left( {\text{x}} \right)f’\left( {\text{x}} \right)$
• $\frac{{\text{d}}}{{{\text{dx}}}}\left[ {\frac{{f\left( {\text{x}} \right)}}{{g\left( {\text{x}} \right)}}} \right] = \frac{{g\left( {\text{x}} \right)f’\left( {\text{x}} \right) – f\left( {\text{x}} \right)g’\left( {\text{x}} \right)}}{{{{\left[ {g\left( {\text{x}} \right)} \right]}^2}}}$
• $\frac{{{\text{dy}}}}{{{\text{dx}}}} = \frac{{{\text{dy}}}}{{{\text{du}}}} \cdot \frac{{{\text{du}}}}{{{\text{dx}}}}$