- total derivative $d$ approximates function with respect to **all** its arguments, not just one - partial derivative $\partial$ does so with respect to just a single variable - in partial derivative $\partial$ you assume other variables as constant - example: - $𝑓(𝑥,𝑦)=2𝑥+3𝑦$ - we compute $\frac{\partial f}{\partial x}$ - $2+\frac{∂(3𝑦)}{∂𝑥}= 2+0 = 2$ - you assume that $y$ stays constant when $x$ changes - in total derivative you're saying that changing $x$ will cause a change in $y$ - $𝑓(𝑥,𝑦)=sin(𝑥)+3y^2$ - $\frac{𝑑𝑓(𝑥,𝑦)}{𝑑𝑥}=cos(𝑥)⋅\frac{𝑑𝑥}{𝑑𝑥}+6𝑦⋅\frac{𝑑𝑦}{𝑑𝑥}$