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Hi! I do not understand the math used in the beginning of this video:

In example 1 (4 minutes in the video), why is it wrong to simply solve the problem like this:

[tex]\vec{V} = [x,-y] \Rightarrow \frac{d\vec{V}}{dt} = [\frac{dx}{dt},-\frac{dy}{dt}] = \vec{a} = [V_x,-V_y][/tex], where V_x and V_y are the velocity-components in the x and y directions, respectively.

I thought you'd only use the chain-rule on non-vector multivariable functions??

EDIT: I'm farily sure the guy did some mistakes.. did he not? Look at his work 5:00 minutes in.

In example 1 (4 minutes in the video), why is it wrong to simply solve the problem like this:

[tex]\vec{V} = [x,-y] \Rightarrow \frac{d\vec{V}}{dt} = [\frac{dx}{dt},-\frac{dy}{dt}] = \vec{a} = [V_x,-V_y][/tex], where V_x and V_y are the velocity-components in the x and y directions, respectively.

I thought you'd only use the chain-rule on non-vector multivariable functions??

EDIT: I'm farily sure the guy did some mistakes.. did he not? Look at his work 5:00 minutes in.

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