Lesson 2.3Product & Quotient Rules

and Higher Derivatives

Product Rule

If a function is the product of 2 functions, the derivative is:

1st ● (derivative of 2nd) + 2nd ● (derivative of 1st)

Example

Quotient Rule

If a function is the quotient of 2 functions, the derivative is:

[bottom ● (derivative of top) − top ● (derivative of bottom)] ÷ bottom2

Mathematical Proofs: The Product Rule

xgxfdxd

Example

Example

More Trig Derivatives

xdxd tan

Draw the position of a ball rolling off a table:

Now try to draw a graph of the velocity of the ball:

Finally, graph the acceleration of the ball:

Higher Order Derivatives

s(t) position

v(t) = s’(t) velocity

a(t) = v’(t) = s’’(t) acceleration

Example

Problem Set 2.3