Example 4-3-7 - Maple Help



Chapter 4: Partial Differentiation



Section 4.3: Chain Rule



Example 4.3.7



 The composition of $f\left(x,y,z\right)=\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}$ with $x\left(r,s\right)={ⅇ}^{r}\mathrm{cos}\left(s\right)$, $y\left(r,s\right)={ⅇ}^{r}\mathrm{sin}\left(s\right)$, $z\left(r,s\right)=rs$ forms the function $F\left(r,s\right)=f\left(x\left(r,s\right),y\left(r,s\right),z\left(r,s\right)\right)$. Obtain the partial derivatives ${F}_{r}$ and ${F}_{s}$ by appropriate forms of the chain rule, and again by writing the rule for $F$ explicitly. Show that the results agree.