Question

differentiate f with respect to x, y, z, and w respectively. f_x = 2x f_y = f_z = f_w =

Explanation:

Step1: Differentiate with respect to x

When differentiating $F = 2x$ with respect to $x$, using the power - rule $\frac{d}{dx}(ax^n)=nax^{n - 1}$ (here $a = 2$ and $n = 1$), we have $F_x=\frac{dF}{dx}=2$.

Step2: Differentiate with respect to y

Since $F$ does not contain $y$, treating $F$ as a constant with respect to $y$, $F_y=\frac{dF}{dy}=0$.

Step3: Differentiate with respect to z

Since $F$ does not contain $z$, treating $F$ as a constant with respect to $z$, $F_z=\frac{dF}{dz}=0$.

Step4: Differentiate with respect to w

Since $F$ does not contain $w$, treating $F$ as a constant with respect to $w$, $F_w=\frac{dF}{dw}=0$.

Answer:

$F_x = 2$, $F_y = 0$, $F_z = 0$, $F_w = 0$