Partial Derivatives: Calculating fₓ and fᵧ (3,1)

[Jessica21]

Hi everyone!

I was wondering if someone could help me with the following question with partial derivatives.

A function f: R^2 -> R is defined by f(x,y) = g(x-2y), where g: R-> R.
If g'(1)= 3, calculate f subscript x (3,1) and f subscript y of (3,1).

thanks!

 

[LCKurtz]

You can use the little X₂ icon to type f_x and f_y.

Do you know the chain rule for this setup:

g is a function of u and u is a function of x and y, then

g_x = ? and g_y = ?

That's what you need.

 

[lanedance]

hi jessica21, welcome to pf ;) usually it helps if you show some working...

i would start by trying to find the partial derviatives of f & thinking about what a partial derviative means

$$f_x = \frac{\partial f}{\partial x} = \frac{\partial }{\partial x} g(x-2y)$$

 

[lanedance]

also remember a partial derivative means the other variables are kept constant in the differentiation