The spadesuit derivative

We first define the function C:  C(t)=h(f(t,2-3t)).

Therefore C(1)=h(f(1,-1))=h(-2)=5 (just looking up the values).

And now the derivative:
This is a triple composition. The 1 comes from the derivative of t with respect to t, and the -3 comes from the derivative of 2-3t with respect to t. And we can get numbers by plugging in t=1:
C´(1)=h´(f(1,-1))(D1f(1,-1)(1)+D2f(1,-1)(-3))=h´(-2)((-5)(1)+(4)(-3))=2(-17)=-34. That's one of the numbers on the left of the handout, so this answer is probably correct!

Maintained by and last modified 2/16/2006.