Show that if (F_{1}, F_{2}), and (F_{3}) are differentiable functions of one variable, then [ operatorname{curl}left(leftlangle F_{1}(x),

Question:

Show that if $F_{1}, F_{2}$, and $F_{3}$ are differentiable functions of one variable, then
\[
\operatorname{curl}\left(\left\langle F_{1}(x), F_{2}(y), F_{3}(z)ightangleight)=\mathbf{0}
\]
Use this to calculate the curl of
\[
\mathbf{F}(x, y, z)=\left\langle x^{2}+y^{2}, \ln y+z^{2}, z^{3} \sin \left(z^{2}ight) e^{z^{3}}ightangle
\]

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