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4.6 Partial differentiation of composite functions

1.

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

2.

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

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

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