Math 1a 2021 Unit 7: Derivative

The derivative is computed for polynomials, exponential and trig functions. By differentiating the Euler formula exp(i a x) = cos(ax) + i sin(ax) one gets the derivatives cos'(ax) = -a sin(ax), sin'(ax) = a cos(ax) for trig functions.
We then look at a few examples.

[sadface]

Professor when we learn functions we were taught they are mappings between sets. What we are not taught is how the relationship between two sets forms a new relationship between two sets, when studying derivatives. As a remark the derivate could not be thought of the as mapping between ordered pairs. It has been useful intutition to think of the derivative as opperation on function (higher order function) and realise that it applies beyond the geometry (tangent) of curve.