Scribe Post for Wednesday October 13th

Today in class we started by looking over our unit quiz again. Mr. O'Brien showed us that nDeriv could be used to solve many of the problems like 1 and 2 if we had time to put the correct formatting into our calculator. Just remember that if you want the derivative at a single point the formatting is for example (Y1,X,10) but if you want to find the derivative at all the points if you wanted to graph it the formatting would be (Y1, X, X) to find the values at all points X. Remember that problems like #7 , the only places that the function is not differentiable is at places that there are vertical tangents, cusps, or places that the functions is not defined.
We then talked about the chain rule.

Mathematical
[f(g(x))]' = f '(g(x)) * g '(x)

Verbal
"The derivative of a composition of functions is the derivative of the outer function evaluated at the inner function times the derivative of the inner function."

Lets look at an example
Ex.

The answer to this is because the outer function is sine,
the inner function is

the derivative of outer = cosine and the derivative of inner = 2x so it’s

derivative of outer evaluated at inner times derivative of inner
cosx²*2x


For more help with the chain rule http://archives.math.utk.edu/visual.calculus/2/chain_rule.4/index.html

The rest of the class we worked on our homework
The quiz on Friday will have chain rule problems on it

Mr. O’Brien says that you have to have the two forms of the derivative memorized the product, quotient, and the chain rule memorized as well as the 6 trig derivatives.