What does differentiation actually mean?

Differentiation is defined as the rate of change of a function. Imagine we had a function f(x), which we shall let equal x2. We all know what the graph of xlooks like.

The derivative of xis 2x. This means that, as the variable x increases, the gradient increases by 2x. In graphing a derivative, effectively the gradient is on the y axis, hence the steeper the curve of y, the higher the derivative.

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