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On the smooth manifold $M$, suppose $v$ is a tangent vector to $x$. How can one show that for a differentiable function $f$ on $M$, non zero in a neighborhood of $x$, $v(\frac{1}{f})$= $- \frac{v(f)}{f(x)²}$

I just began studying tangent vector on smooth manifold and besides using Leibniz rule and linearity of $v$ I have no idea how to proceed

guest
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1 Answers1

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Hint: Apply v on $1 = \frac{f}{f} = f \frac{1}{f}$ and use the Leibniz rule.

Dominik
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