$\mathrm{df}$

$\=f_x\left(15\,6\,21\right)\cdot \left(\pm 0.2\right)\+f_y\left(15\,6\,21\right)\cdot \left(\pm 0.2\right)\+f_z\left(15\,6\,21\right)\cdot \left(\pm 0.2\right)$

$\=\left(54\+72\+42\right)\cdot \left(\pm 0.2\right)$

$\= \pm 33.6$

Define $f\left(x\,y\,z\right)$ and its first partial derivatives

$f\left(x\,y\,z\right)\=2\left(y z\+x z\+x y\right)$$\stackrel{\text{assign as function}}{\to }$$f$

Calculate $f\left(2.03\,3.12\,1.48\right)\doteq f\left(2\,3\,3\/2\right)\+\mathrm{df}$ 

$\mathrm{f\_\_x}\left(15\,6\,21\right)\cdot \left(.2\right)\+\mathrm{f\_\_y}\left(15\,6\,21\right)\cdot \left(.2\right)\+\mathrm{f\_\_z}\left(15\,6\,21\right)\cdot \left(.2\right)$ = $33.6$

Compute $\mathrm{\Δ}f$ "exactly"

$f\left(15.2\,6.2\,21.2\right)-f\left(15\,6\,21\right)$ = $33.84$

$f≔\left(x\,y\,z\right)\to 2\left(y z\+x z\+x y\right)\:$

$\mathrm{df}≔{\mathrm{D}}_1\left(f\right)\left(15\,6\,21\right)\cdot \left(.2\right)\+{\mathrm{D}}_2\left(f\right)\left(15\,6\,21\right)\cdot \left(.2\right)\+{\mathrm{D}}_3\left(f\right)\left(15\,6\,21\right)\cdot \left(.2\right)$ = $33.6$