What is Differentiation ?
Given a function and a specific point, the differentiation at that point is the slope of a tangent line at that point.
If f(x) is the original function, then the differentiation of f is f'(x) (pronounced f prime) or df/dx
The derivative is sometimes called the slope of the tangent line to the graph at a particular point.
The differentation is also commonly called the derivative
This deriavative is a linear operator that inputs a function and returns another function.
This is in contrast to an algebraic equation that inputs a number and returns another number.
y = mx + c
A line through 2 points on a curve is called a secant line
example - x squared
derivative is 2x
example - x cubed - x squared + 4x -3
Derivative of Ln
Derivative of Ln with functional argument
Derivative of e
Derivative of e with functional argument
The derivative of e with a functional exponent is equal to e with that derivative of that exponent.
We can use the chain rule here because we have a composite function.