The plane $y = −2$ intersects the surface
$$ z = x^3 − y \sin(x + y) $$
in a curve.
What is the slope of the tangent line to this intersection curve at the point $(2, −2, 8)$?
I've tried substituting in $y = -2$ and then finding the derivative of that but I don't think it's right but I'm not too sure what else to do.
\begin{gather} z=x^3-y\sin(x+y)\\ z=x^3+2\sin(x-2)\\ \frac{dz}{dx}=3x^2+2\cos(x-2)=14 \end{gather}