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Introduction to Derivatives

Introduction to Derivatives

Prerequisites Required- Basic Mathematics

Suppose we have a basic linear function, $f(x) = 4x + 2$

Figure 1: Plot of the function $f(x) = 4x + 2$.

The slope of this function is $4$ (if the input $x$ increases by 1, the output increases by $4$).

The derivative of a function is its slope (change in output per change in input). This calculation is very easy for linear functions because the slope is the same everywhere.

For the function $f(x) = 4x + 2$, its slope with respect to $x$ is 4.

Figure 2: Visual depiction of rise vs run of the function $f(x) = 4x + 2$ to calculate the function's slope.

Jonathan Bowen