Partial Derivatives

Gradients are a combination of Partial Derivatives.

$\frac{\partial y}{dx}=Y_{x}$ and Vise Versa

Getting a parallel plane with a point

Plug point into the equation, get num. set num equal to equation, cross multiply.

Decreasing

Glorified Gradient, -Gradient is the Decreasing rate and Pos is the increasing.

Linear Approximation:

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Implicit Differentiation

When there is another variable not listed..

Find how Z changed with respect to x/y, make sure to segregate the problem.

partially derive z and x/y.

Directional Gradient

$\displaylines{D_{u}f\left(p\right)=\Delta f\left(p\right)\cdot u}$

u is unit vector, or direction. MAKE SURE ITS A UNIT VECTOR.