Question

What happens if we differentiate a vector expressed as a cross product of two vectos?

Answer 1

Answer:

On differentiating a cross product we end up using the Product rule or the uv method.

Let the Cross product be u × v

$\implies \dfrac{d}{dx} [ u \times v ] \\\\\text{Applying Product Rule or UV method we get,}\\\\\implies \dfrac{d}{dx} [ u \times v ] = \dfrac{du}{dt} \times v + \dfrac{dv}{dt} \times u \\\\\implies \dfrac{d}{dx} [ u \times v ] = v \dfrac{du}{dt} + u \dfrac{dv}{dt}$

Hence this is the required answer.