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Tangent to a curve

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)

Physical InterpretationEdit

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)

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