数学题在线解答

问题:求导e^tan1/x*sin1/x

解答

求导 y=e^{\tan{\frac{1}{x}}} \cdot \sin { \frac {1} {x} }

\begin{aligned}
y^{\prime}
&=-\frac{1}{x^{2}\cos^2\frac{1}{x}} \cdot \mathrm{e}^{\tan\frac{1}{x}} \cdot \sin \left(\frac{1}{x}\right)-\frac{1}{x^{2}} \cdot \mathrm{e}^{\tan\frac{1}{x}} \cdot \cos \left(\frac{1}{x}\right)\\
&=-\frac{1}{x^{2}} \cdot \mathrm{e}^{\tan\frac{1}{x}} \cdot\left(\tan \left(\frac{1}{x}\right)\sec\left(\frac{1}{x}\right)+\cos \left(\frac{1}{x}\right)\right)
\end{aligned}

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