3 La Derivada

3.1 Derivada simple

\[ y = f(s) = 2x^4 + 3x^2 + 6x +1 \Rightarrow \frac{dy}{dx} = 8x^3 + 6x + 6 \]

3.2 Regla de la cadena

\[ z = f(x(t), y(t)) \longrightarrow \frac{dz}{dt} = \frac{\partial f}{\partial x}\frac{dx}{dt} + \frac{\partial f}{\partial y}\frac{dy}{dt} \]

3.3 Gradiente de una función

\[ grad(\phi) = \frac{\partial \phi}{\partial x} \overrightarrow{i} + \frac{\partial \phi}{\partial y} \overrightarrow{j} + \frac{\partial \phi}{\partial z} \overrightarrow{k} \]