Differentiating the Sum of Two Functions

Find the derivative of \(f( x) =3x^{2}+8\).

Solution Here, \(f\) is the sum of \(3x^{2}\) and \(8\). So, we begin by using the Sum Rule. \[ \begin{eqnarray*} &&f^\prime ( x) =\dfrac{d}{dx} ( 3x^{2}+8 ) \underset{\underset{{\color{#0066A7}{\hbox{ Sum Rule}}}}{\color{#0066A7}{\uparrow}}}{=} \dfrac{d}{dx} ( 3x^{2} ) + \dfrac{d}{dx}8 \underset{\underset{\underset{{\color{#0066A7}{\hbox{ Multiple Rule}}}}{\color{#0066A7}{\hbox{ Constant}}}}{\color{#0066A7}{\uparrow }}}{=} 3\dfrac{d}{dx}x^{2}+0 \underset{\underset{\underset{{\color{#0066A7}{\hbox{ Power Rule}}}}{\color{#0066A7}{\hbox{ Simple}}}}{\color{#0066A7}{\uparrow}}}{=} 3\cdot 2x=6x \end{eqnarray*} \]