Measuring error analysis with 3 variables

[getty102]

Homework Statement

Consider the function F(xyz)=x^4+5y^4+2yz+3. Let the uncertainty in x be represented by the variable dx, the uncertainty in y be represented by the variable dy, and the uncertainty in z be represented by the variable dz.
Find an algebraic expression for the uncertainty in the function due to the uncertainty in x

Homework Equations

Δf_x(x,y,z)=f(x+Δx,y,z)−f(x,y,z)

The Attempt at a Solution

ΔF_x = [((x+dx)^4)+(5*(y^4))+(2*y*z)+3]-[(x^4)+(5*(y^4))+(2*y*z)+3]
I simply added dx to the variable x although this is not correct

 

[Simon Bridge]

I simply added dx to the variable x although this is not correct

In what way is this not correct?