Derivatives
The definition of the derivative
We compute the instantaneous growth rate by computing the limit of average growth
rates.
The derivative as a function
Here we study the derivative of a function, as a function, in its own right.
Differentiability implies continuity
We see that if a function is differentiable at a point, then it must be continuous at
that point.
Derivatives of products are tricky
Two young mathematicians discuss derivatives of products and products of
derivatives.
The Product rule and quotient rule
Here we compute derivatives of products and quotients of functions
Derivatives of trigonometric functions
We use the product and quotient rule to unleash the derivatives of the trigonometric
functions.
Rates of rates
Two young mathematicians look at graph of a function, its first derivative, and its
second derivative.
Position, velocity, and acceleration
Here we discuss how position, velocity, and acceleration relate to higher
derivatives.