Differentiation

Can you hit the target functions using a set of input functions and a little calculus and algebra?

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?