Verifying solutions to differential equations and using ansatzes

Taylor polynomial calculation shortcuts - example 2

Taylor polynomial - an application to calculating a series

Taylor polynomial calculation shortcuts - theory and an example

An applied optimization problem

Optimization - a geometric example

Strategies for setting up applied optimization problems

Calculating the global maximum for a two-variable function

Logarithmic differentiation

Phase lines as a qualitative tool for analyzing differential equations

Solving linear ODEs using a phase-line inspired method

Some modelling applications that lead to linear (and one non-linear) differential equations

Slope fields as a qualitative tool to understand solutions to differential equations

Verifying solutions to differential equations and using ansatzes

Sketching Graphs - Rational Power Functions

Sketching Graphs - Critical points that are neither minima, maxima, nor inflection points.

Sketching Graphs - Minimum, Maximum, or Inflection point

The general product rule

Derivative notation

Finding the derivative of an inverse function

Implicit differentiation - infinite slopes on relations

Finding the derivative of arcsin(x)

More derivatives using logarithms - the general power rule and (x^x)'

Implicit differentiation

Exponential functions and their derivatives