Question

Find the derivative by first principle in examples to $\left(8\right)$
$\cos x$

Answer 1

${lim}_{h\to 0}\frac{\cos (x+h)-\cos x}{h}{lim}_{h\to 0}\frac{\cos x\cos h-\sin x\sin h-\cos x}{h}{lim}_{h\to 0}\frac{\cos x(\cos h-1)}{h}-{lim}_{h\to 0}\frac{\sin x\sin h}{h}0-\sin x=-\sin x$