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Differentiation From First Principles

Differentiating a linear function A straight line has a constant gradient, or in other words, the rate of change of y with respect to x is a constant.

Example

Consider the straight line y = 3x + 2 shown below

A graph of the straight line y = 3x + 2.

We can calculate the gradient of this line as follows. We take two points and calculate the change in y divided by the change in x.

When x ...

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