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Question Number 194386 by SANOGO last updated on 05/Jul/23

$$calculthethederiveof$$$${cos}^3{\left(\frac{\theta }{3}\right)}^{\prime }$$

Answered by Frix last updated on 05/Jul/23

$$f\left(t\right)=t^3$$$$g\left(t\right)=\cos t$$$$h\left(t\right)=\frac{t}{3}$$$${\left(f\left(g\left(h\left(t\right)\right)\right)\right)}^{\prime }=h^{\prime }\left(t\right)\times g^{\prime }\left(h\left(t\right)\right)\times f^{\prime }\left(g\left(h\left(t\right)\right)\right)$$$$\mathrm{W}e\mathrm{get}$$$$\frac{1}{3}\times (-\sin \frac{\theta }{3})\times {3\cos }^2\frac{\theta }{3}=-\sin \frac{\theta }{3}{\cos }^2\frac{\theta }{3}$$

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