Posts in Learn math
Partial derivatives in two variable functions

Finding derivatives of a multivariable function means we’re going to take the derivative with respect to one variable at a time. For example, we’ll take the derivative with respect to x while we treat y as a constant, then we’ll take another derivative of the original function, this one with respect to y while we treat x as a constant.

Learn mathKrista King
Finding inverse trig derivatives

To avoid confusion between negative exponents and inverse functions, sometimes it’s safer to write arcsin instead of sin^(-1) when you’re talking about the inverse sine function. The same thinking applies to the other five inverse trig functions.

Simple equations with subscripts

Why use subscripts instead of different variables? Well, the variables in science often represent something specific. For example, P stands for pressure and in some equations you’ll have more than one pressure represented. In that case we use subscripts: P_1, P_2, P_3, and so on.

Learn mathKrista King
How to find the orthogonal trajectories

The orthogonal trajectories to a family of curves are the curves that intersect each member of the family at a perfectly perpendicular angle. So given a family of curves, you can change the value of the constant in the equation that models the family, to create a family of many curves, and then sketch the family in the plane.

Learn mathKrista King
U-substitution to solve integrals

Most integrals need some work before you can even begin the integration. They have to be transformed or manipulated in order to reduce the function’s form into some simpler form. U-substitution is the simplest tool we have to transform integrals.