First Principles Differentiation - Trigonometry (Edexcel A-Level Mathematics): Flashcards

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

$\frac{d}{dx} \sin(x) = \cos(x)$

$\sin(x+h) = \sin(x)\cos(h) + \cos(x)\sin(h)$

$\lim_{h \to 0} \sin(h)/h = 1$

The limit is $0$; it's the derivative of $\cos$ at $x=0$.

$\frac{d}{dx} \cos(x) = -\sin(x)$

$\frac{d}{dx} \tan(x) = \sec^2(x)$

$\frac{d}{dx} \sec(x) = \sec(x)\tan(x)$

When $\frac{dy}{dx} = 0$

$\frac{d}{dx} \sin(x) = \cos(x)$, $\frac{d}{dx} \cos(x) = -\sin(x)$