University⏱ 4 min

Derivative as Slope

What a derivative visually means

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Function

Move point (x)

x1.00

Derivative

ddx[x2]=2x\frac{d}{dx}\left[x^2\right] = 2x

Slope at point

f′(1.00)=2.000f'(1.00) = 2.000

Intuition

The pink dashed line is the tangent - its slope shows how fast the function changes at this point. That is the derivative.