Warm UpSuppose it costs to produce x dishwashers. a. Find the average cost of producing 100

dishwashers.

b. Find the marginal cost when producing 100 dishwashers.

3.5 – Derivatives of Trig Functions

Goal• I will be able to derive derivatives of all 6 basic trig functions. I will

also define Jerk.

What are the 6 basic trig functions?

Good News!• You only have to memorize 2 derivatives, the rest are very easy to

derive.

• Hand out

Tools we now have:Constant, Power, Product, Quotient, Trig.

We will be combining these rules in single problems.

Example

• What rules do we need?

• Power, product, trig.

• Solution:

You try!

What rules will you be using?

Definition• A sudden change in acceleration is called jerk. It is the derivative of

acceleration, or the third derivative of position.

Recaps(t)=positions’(t)=v(t)=velocitys’’(t)=v’(t)=a(t)=accelerations’’’(t)=v’’(t)=a’(t)=j(t)=jerk

Example• The position of the of a weight on a spring is given by

Find the velocity, acceleration and jerk at a time t.

You try

Homework• All problems on calendar. We will answer questions tomorrow, so

make sure you attempt the problems tonight .