Formulae To Remember

Key Calculus for A Level: Differentiation

Differentiation

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

\frac{d}{d x} e^{k} x = k e^{x}

\frac{d}{d x} l n (x) = 1 / x

\frac{d}{d x} (a x^{2} + b x + c) = 2 a x + b

Differentiation of Trigonometric Ratios

\frac{d}{d x} \sin k x = k \cos k x

\frac{d}{d x} \cos k x = - k \sin k x

The Chain Rule

The Product Rule

\frac{d y}{d x} = u \frac{d v}{d x} + v \frac{d u}{d x}

w h e r e u a n d v a r e f u n c t i o n s o f x a n d y = u v

The Quotient Rule

\frac{d y}{d x} = \frac{u \frac{d u}{d x} - v \frac{d u}{d x}}{v^{2}}

w h e r e u a n d v a r e f u n c t i o n s o f x a n d

y = \frac{u}{v}

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