https://3speak.tv/watch?v=mes/hfsetrue
In this video I go further into vector functions and this time show how to obtain their derivatives and integrals. The definition of derivative for a vector function is much the same as with a real valued function, but the difference is that we apply this definition to each component of the vector function. I also show this geometrically as a tangent vector to a point on a 3D surface and the limit as the second vector between that point and another point on the surface approach each other. The differentiation rules, such as the chain rule and product rule of dot products and cross products, have their similar counterparts for vector functions as well. Likewise, integration is also similar to real valued functions but the integral of each component is solved. This will be the basis for future videos when I cover velocity and acceleration of planetary bodies so stay tuned for that!
#math #science #calculus #vectorfunctions #education
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