Differentiating Rational Powers (VCE SSCE Mathematical Methods): Flashcards

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

$ax^{a-1}$

$\frac{1}{2}x^{-\frac{1}{2}}$ or $\frac{1}{2\sqrt{x}}$

$\frac{1}{3}x^{-\frac{2}{3}}$

$\frac{dy}{dx} = \frac{1}{\frac{dx}{dy}}$

$\frac{1}{n}x^{\frac{1}{n}-1}$

$x > 0$ (positive real numbers)

Vertical (along the $y$-axis)

$x^{\frac{m}{n}}$

Derivative undefined (division by zero)