Jacobian of a system of equations

Question

I'm asked to compute the Jacobian of a system of equations

$x_1^4+x_2^4-1=0$
$x_2-\sin(5x_1)=0$
$x_1-x_3^2=0$

What's the Jacobian of a system of equations?
Do I perhaps need to infer the individual rows as individual functions?

Answer 1

Define $F(x_1, x_2, x_3) = (x_1^4+x_2^4-1, x_2 - \sin(5 x_1), x_1 - x_3^2)$ then equation is $F(x_1, x_2, x_3) = 0$. Find Jacobian of $F.$