Derivatives formula sheet

24 rows · CalcRef · sample of the first 6 rows

Derivatives
Formula	Statement	Conditions
Limit Definition of Derivative	$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$	no restriction stated
Constant Rule	$\frac{d}{dx}[c] = 0$	no restriction stated
Power Rule	$\frac{d}{dx}[x^n] = nx^{n-1}$	n can be any real number. For n = 0 the result is 0. For integer n the rule holds wherever x^n is defined; for non-integer n, x^n and the rule require x > 0.
Constant Multiple Rule	$\frac{d}{dx}[c \cdot f(x)] = c \cdot f'(x)$	no restriction stated
Sum/Difference Rule	$\frac{d}{dx}[f(x) \pm g(x)] = f'(x) \pm g'(x)$	no restriction stated
Product Rule	$\frac{d}{dx}[f(x) \cdot g(x)] = f'(x)g(x) + f(x)g'(x)$	no restriction stated

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