Miscellaneous Exercises (VCE SSCE Mathematical Methods): Flashcards

Recognise derivative patterns and work backwards

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

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

Both equal $\frac{\sqrt{2}}{2}$

$x \log_e(kx) - x + c$

$\frac{1}{2}x^2 \log_e(kx) - \frac{x^2}{4} + c$

$e^{-x^2}$

Complex expressions, verification, non-elementary functions

Product rule

Differentiate the result to check it matches the integrand