- #1
mathmari
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MHB
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Hey! ![Eek! :eek: :eek:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
How could we prove the following rule for differentiable curves in $\mathbb{R}^3$ ?? (Wondering)
$$\frac{d}{dt}[\overrightarrow{\sigma}(t)\times \overrightarrow{\rho}(t)]=\frac{d\overrightarrow{\sigma}}{dt}\times \overrightarrow{\rho}(t)+\overrightarrow{\sigma}(t)\times \frac{d\overrightarrow{\rho}}{dt}$$
How could we prove the following rule for differentiable curves in $\mathbb{R}^3$ ?? (Wondering)
$$\frac{d}{dt}[\overrightarrow{\sigma}(t)\times \overrightarrow{\rho}(t)]=\frac{d\overrightarrow{\sigma}}{dt}\times \overrightarrow{\rho}(t)+\overrightarrow{\sigma}(t)\times \frac{d\overrightarrow{\rho}}{dt}$$