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}}}}