Calculating Derivatives of f(x,y) with Respect to x

[CStudy]

I am having difficulty trying to figure the following .

What is $$\frac{\mathrm{d} }{\mathrm{d} x}f(x,y)$$ where x is a function of s and t.

Here is my calculation $$\frac{\mathrm{d} }{\mathrm{d} x}f(x(s,t),y) = \frac{\partial f}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f}{\partial x}\frac{\partial x}{\partial s}$$

Does this seem correct?

 

[FactChecker]

That seems wrong. df/dx is just the change of f per unit change of x. It doesn't matter that x is a function of s and t. Once you figure out what df/dx is and you want to evaluate it at some value of x, then you can worry about x being a function of s and t.

PS. f is actually a function of both x and y, so it is a partial derivative on the left ∂f/∂x.