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![\bf g(t)=5cos^2(\pi t)\iff g(t)=5[cos(\pi t)]^2\\\\ -----------------------------\\\\ \textit{thus, using the chain-rule} \\\\\\ \cfrac{dg}{dt}=5\cdot 2cos(\pi t)^1\cdot \pi \cdot t^0\implies \cfrac{dg}{dt}=10\pi cos(\pi t)](/tpl/images/0406/5540/0a29a.png)
![\bf cos^5\left( \frac{2\pi }{3}\theta \right)\iff \left[ cos\left( \frac{2\pi }{3}\theta \right) \right]^5](/tpl/images/0406/5540/c7849.png)
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G(t)=5cos^2(pi)(t) using the chain rule...
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