The Five Derivative Rules

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Memorize

These five solve 90% of CSCA calculus. Power rule alone covers the most. Not negotiable — drill them.

\frac{d}{d x} (x^{n}) = n x^{n - 1}

The Power Rule — most-used derivative formula on CSCA

Power

$\frac{d}{d x} (x^{n}) = n x^{n - 1}$

Bring exponent down, subtract 1

Sum

$(f + g)^{'} = f^{'} + g^{'}$

Differentiate term by term

Chain

$(f (g (x)))^{'} = f^{'} (g) \cdot g^{'} (x)$

Outside × inside derivative