Two young mathematicians discuss the novel idea of the ‘‘slope of a curve.’’

We compute the instantaneous growth rate by computing the limit of average growth rates.

Here we’ll practice finding the derivative using limits.

Two young mathematicians discuss derivatives as functions.

Here we study the derivative of a function, as a function, in its own right.

We see that if a function is differentiable at a point, then it must be continuous at that point.

Two young mathematicians think about ‘‘short cuts’’ for differentiation.

We derive the constant rule, power rule, and sum rule.

Two young mathematicians discuss derivatives of products and products of derivatives.

Here we compute derivatives of products and quotients of functions

We derive the derivative of sine.

We use the product and quotient rule to unleash the derivatives of the trigonometric functions.

Two young mathematicians look at graph of a function, its first derivative, and its second derivative.

Here we look at graphs of higher order derivatives.

Here we discuss how position, velocity, and acceleration relate to higher derivatives.