It is so complecated for me. Please can you show how to solve. Thank you.
2026-05-05 20:08:00.1778011680
Problem about tangent vector and the inclusion map of the unit circle.
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We have $$i_*\left(\frac{\partial}{\partial \bar{x}}\right)(x) = \frac{\partial}{\partial \bar{x}}(i^*x)$$ and likewise $$i_*\left(\frac{\partial}{\partial \bar{x}}\right)(y) = \frac{\partial}{\partial \bar{x}}(i^*y).$$
Given that the text defines $\bar{x}=i^*x$ and $\bar{y}=i^*y$, can you solve it from here?
The complete solution for $x$: $$i_*\left(\frac{\partial}{\partial\bar{x}}\right)(x) = \frac{\partial}{\partial\bar{x}}(i^*x) = \frac{\partial}{\partial\bar{x}}(\bar{x})=1$$