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Question Number 195136 by mathlove last updated on 25/Jul/23

$$f\left(x\right)=arctan\left(sinx\right)$$$$andcosa=\frac{2}{3}faind{f}^{{}^{\prime }}\left(a\right)=?$$

Answered by som(math1967) last updated on 25/Jul/23

$$\mathit{f}{}^{\prime }\left(x\right)=\frac{1}{1+{\mathit{s}\mathit{i}\mathit{n}}^2\mathit{x}}\times \mathit{c}\mathit{o}\mathit{s}\mathit{x}$$$$\mathit{f}{}^{\prime }\left(\mathit{\alpha }\right)=\frac{1}{1+{\mathit{s}\mathit{i}\mathit{n}}^2\mathit{\alpha }}\times \mathit{c}\mathit{o}\mathit{s}\mathit{\alpha }$$$$=\frac{1}{1+\frac{5}{9}}\times \frac{2}{3}$$$$=\frac{9}{14}\times \frac{2}{3}=\frac{3}{7}$$

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