In Terry Tao's notes on the Poincare Conjecture http://terrytao.wordpress.com/2008/03/28/285glecture1ricciflow/#more293 He makes a jump I can't understand! From differentiating the identity $g^{\alpha \beta}g_{\beta \gamma} = \delta^\alpha_\gamma$ we obtain the variation formula $\frac{d}{dt}g^{\alpha \beta} =g^{\alpha \gamma}g^{\beta \delta}\dot{g}_{\gamma \delta} $ But I don't understand this leap. Can anyone show me what I'm supposed to be doing, I'm familiar with tensors and the variational calculus but putting the two together is hard for me.
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