Find the follow derivatives:
$\frac{dz}{ds}$ and $\frac{dz}{dt}$, where $z = sin(2x+y)$, $x = s^2 - t^2$, and $y = s^2 + t^2$
Solution attempt:
$\frac{dz}{ds} = \frac{dz}{dx} \cdot \frac{dx}{ds} + \frac{dz}{dy} \cdot \frac{dy}{ds} = 4s(cos(2x+y)) + cos(2x+y) \cdot 2s = 6s \cdot cos(2x+y)$
$\frac{dz}{dt} = \frac{dz}{dx} \cdot \frac{dx}{dt} + \frac{dz}{dy} \cdot \frac{dy}{dt} = 2 cos(2x+y) \cdot (-2t) + cos(2x+y) \cdot (2t) = -2tcos(2x+y)$