Product Rule (Leaving Cert Mathematics): Flashcards

Differentiating the product of two functions

$\frac{dy}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}$

$\frac{dy}{dx}=u'v+uv'$

$u=x^2$, $v=\sin(x)$

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

$u=e^x$, $v=\ln(x)$

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

$u=x^2$, $v=\sqrt{3x+1}$

$\frac{15x^2+4x}{2\sqrt{3x+1}}$

$\cos(x)$