Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives-of-vector-valued-functions/v/partial-derivatives-of-vector-fields-component-by-component Here we step through each partial derivative of each component in a vector field, and understand what each means geometrically.