blamocur
Elite Member
- Joined
- Oct 30, 2021
- Messages
- 2,627
You case has 3 and 2 variables:
[math]F(x,y) = f(p(x,y), q(x,y), r(x,y))[/math]and the chain rule for [imath]F_x[/imath] is:
[math]\frac{\partial F}{\partial x} = \frac{\partial F}{\partial p} \cdot \frac{\partial p}{\partial x} + \frac{\partial F}{\partial q} \cdot \frac{\partial q}{\partial x} + \frac{\partial F}{\partial r} \cdot \frac{\partial r}{\partial x}[/math]Can you work out or find the formula for [imath]F_y[/imath]?
Your case is somewhat simpler: [imath]p[/imath] and [imath]q[/imath] are trivial, and [imath]r[/imath] is called [imath]g[/imath].
[math]F(x,y) = f(p(x,y), q(x,y), r(x,y))[/math]and the chain rule for [imath]F_x[/imath] is:
[math]\frac{\partial F}{\partial x} = \frac{\partial F}{\partial p} \cdot \frac{\partial p}{\partial x} + \frac{\partial F}{\partial q} \cdot \frac{\partial q}{\partial x} + \frac{\partial F}{\partial r} \cdot \frac{\partial r}{\partial x}[/math]Can you work out or find the formula for [imath]F_y[/imath]?
Your case is somewhat simpler: [imath]p[/imath] and [imath]q[/imath] are trivial, and [imath]r[/imath] is called [imath]g[/imath].
