Derivatives

Definition of the derivative

Slope of a curve

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

The definition of the derivative

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

Definition of the Derivative

Here we’ll practice finding the derivative using limits.

Derivatives as functions

Wait for the right moment

Two young mathematicians discuss derivatives as functions.

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.

Rules of differentiation

Patterns in derivatives

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

Basic rules of differentiation

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

Product rule and quotient rule

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

The derivative of sine and cosine

We derive the derivative of sine.

Derivatives of trigonometric functions

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

Higher order derivatives and graphs

Rates of rates

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

Higher order derivatives and graphs

Here we look at graphs of higher order derivatives.

Position, velocity, and acceleration

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

End of Content for Exam 3


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