$[10]4.$ Use implicit differentiation on these.

a$)$ Find an expression for $d\frac{y}{d}x$ at any point on the curve $cos(y^2)+e^{3x+2y}=8.$

b$)$ For the curve $x^2-4x{y}^2=y^3+9,$ do the following:

$($i$)$ Show that the point $(-1,2)$ is on the curve.

$($ii$)$ Find an equation for the line that's tangent to the curve at $(-1,2).$