Multivariable Derivatives

#Math

$\displaystyle \exists f(x,y)\rightarrow f_{x}=\frac{ \partial f }{ \partial x },f_{y}=\frac{ \partial f }{ \partial y }$

$\displaystyle \frac{ \mathrm{d}f }{ \mathrm{d}s }=\nabla_{\vec{u}}f=\nabla f\cdot \frac{\vec{u}}{\lvert \vec{u}\rvert}=\nabla f\cdot \hat{u}=\lvert \nabla f\rvert\cos \theta$

• This is the directional derivative of $\displaystyle f$ in the direction of $\displaystyle \vec{u}$