① Derivada

Apuntes

① Derivadas parciales directas y mayor orden a) $f(x,y) = \cos xy + e^{ix} + x^2y^3$ $$ \frac{\partial f}{\partial x} = \frac{\partial f}{\partial y} = F_{xx} = F_{xy} = F_{yx} $$ b) $W = xyz^3$ $$ \frac{\partial w}{\partial x}, \frac{\partial w}{\partial y}, \frac{\partial w}{\partial z} $$ ② Derivadas Implícitas $$ 2x + 3z = x^2z^2 + z^3 + xz $$ $$ \begin{array}{l} \frac{\partial \text{ término}}{\partial V.I.} + \frac{\partial \text{ término}}{\partial V.D.} \left( \frac{\partial V.D.}{\partial W.I.} \right) \\ \text{v. p.} \\ \text{V.I.} \frac{\partial z}{\partial x} = \\ \frac{\partial x}{\partial z} = \\ \end{array} $$ ③ Regla de la cadena de varios variables $$ W = xyz^3 $$ $$ \begin{array}{l} x = \cos 3r + \cos 6 \\ y = e^r \\ z = 4r^3 \\ \end{array} $$