Product Rule (Edexcel A-Level Mathematics): Flashcards

$\frac{d}{dx}[u(x)v(x)] = u'v + uv'$

If $u$ and $v$ are functions, $d(uv)/dx = u'v + uv'$.

$u'(x) = 2x$

$v'(x) = \cos(x)$

$\frac{dy}{dx} = 2x\sin(x) + x^2\cos(x)$

$dy/dx = e^x(\ln(x) + 1/x)$

$\frac{dy}{dx} = (6x + 2)\cos(x) - (3x^2 + 2x)\sin(x)$

$\frac{dy}{dx} = e^{3x}(2x + 3x^2)$

$f(x)g'(x) + g(x)f'(x)$ for functions $f$ and $g$.

Identify $u$ and $v$, then apply the product rule.