Multivariable Derivatives

$\exists f(x,y)\to f_x=\frac{\partial f}{\partial x},f_y=\frac{\partial f}{\partial y}$

$\frac{\mathrm{d}f}{\mathrm{d}s}={\nabla }_{\vec{u}}f=\nabla f\cdot \frac{\vec{u}}{|\vec{u}|}=\nabla f\cdot \hat{u}=|\nabla f|\cos \theta$

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