Example 4-3-6 - Maple Help



Chapter 4: Partial Differentiation



Section 4.3: Chain Rule



Example 4.3.6



 The composition of $f\left(x,y\right)=\mathrm{ln}\left(3{x}^{2}+4{y}^{2}\right)$ with  forms the function $F\left(r,s\right)=f\left(x\left(r,s\right),y\left(r,s\right)\right)$. 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.