Example 4-3-3 - Maple Help



Chapter 4: Partial Differentiation



Section 4.3: Chain Rule



Example 4.3.3



 The composition of $f\left(x,y\right)=\mathrm{ln}\left(2y+\sqrt{1-{x}^{2}}\right)$ with $x\left(t\right)={t}^{2}$, $y\left(t\right)=\mathrm{sin}\left(t\right)$ forms the function $F\left(t\right)=f\left(x\left(t\right),y\left(t\right)\right)$. Obtain $F\prime \left(t\right)$ by an appropriate form of the chain rule, and again by writing the rule for $F$ explicitly. Show that the results agree.