Derivative Notation and Basic Rules (HSC SSCE Mathematics Advanced): Flashcards

$f'(x) = nx^{n-1}$

Bring down exponent, reduce exponent by one

Positive integers, negatives, fractions

$x^{\frac{1}{2}}$

$x^{-n}$

$\frac{d}{dx}[k \times f(x)] = k \times f'(x)$

$\frac{d}{dx}[f(x) \pm g(x)] = f'(x) \pm g'(x)$

Rate of change of $y$ with respect to $x$

Derivative operator

Zero