Product Rule (AQA A-Level Mathematics): Flashcards

$u \cdot v' + v \cdot u'$

$vu' + uv'$

$u$ changing while $v$ stays constant, and $v$ changing while $u$ stays constant

$x^2 \cos(x) + 2x \sin(x)$

$\frac{e^x}{x} + e^x \ln(x)$

$-(3x^2 + 2x)\sin(x) + (6x + 2)\cos(x)$

$e^{3x}(3x^2 + 2x)$

$\sin x + x \cos x$

$6x^3 e^{2x+3}(2 + x)$

$\frac{1}{2}x(3x+1)^{-\frac{1}{2}}(15x+4)$