Partial Derivative of a vector product

Question

What is the partial derivative of a dot or a cross vector product?

Answer 1

For vector valued function the product rule applies to dot and cross product when the partial derivative is involved.

$$ \frac \partial{\partial x }(f.g) = f. \left (\frac {\partial g}{\partial x }\right)+ \left (\frac {\partial f}{\partial x }\right).g $$

$$\frac \partial{\partial x } (f\times g) = f\times \left (\frac {\partial g}{\partial x }\right)+ \left (\frac {\partial f}{\partial x }\right)\times g $$