## FANDOM

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Simply, the derivative of is the slope or rate of change of a function at a certain point. Unlike the relative and average change $\frac{\Delta y}{\Delta x}$, the derivative is the instantaneous rate $\frac{dy}{dx}$

$f'(x_0)$, the derivative of $f(x)$ at $x_0$, is the slope of the tangent line to $y=f(x)$ at $P$.

The derivative is used in classical physics, chemistry, and GPS.

There are two interpretations of a derivative: geometric and physical

## Geometric InterpretationEdit

Find the tangent line to $y=f(x)$ at $P=(x_0,y_0)$

## General Rules Edit

Product Rule $(uv)' = u'v + uv'$

Quotient Rule $\left ( \frac{u}{v} \right ) = \frac{u'v - uv'}{v^2}$

Constant Multiple Rule $\frac{d}{dx} \left ( c \cdot f(x) \right ) = c \cdot \frac{d}{dx} f(x)$