I am attempting to work my way through the product rule for inner products, using the properties of linearity and symmetry. I am wondering if the following step is allowed, exploiting the bilinear property:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(t) = \left\langle{\alpha}(t),{\beta}(t)\right\rangle \rightarrow f'(t) = \lim_{h \to 0}\frac{1}{h}[\left\langle{\alpha}(t + h),{\beta}(t + h)\right\rangle - \left\langle{\alpha}(t),{\beta}(t)\right\rangle][/tex]

If so, I think I can proceed using similar tricks from the proof of the product rule for "ordinary" functions . If not, I am lost on how to proceed.

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# Differentiating an Inner Product

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