4.6 Partial differentiation of composite functions

1.

(a) $${8t + 6t^{2}}$$ (b) $${0}$$ (c) $${\cos{2t} + \sin{2t}}$$ (d) $${12t^{11}}$$

2.

(a) $${z_{u} = 10u, z_{v} = 10v}$$

(b) $${z_{u} = 2u + 2v + 2uv + v^{2} + 4uv^{2}, z_{v} = 2u + 2v + 2uv + u^{2} + 4u^{2}v}$$　

(c) $${z_{u} = 2uv^{6}, z_{v} = 6u^{2}v^{5}}$$