Question

Посчитайте $f'(0)$

a)$f(x)=(x^{2}-1)cos(x)$

d)$f(x)=\frac{sin(x)}{1-5x}$

Answer 1

Ответ:

$f(x)=(x^2-1)\cdot cos0=(x^2-1)\cdot 1=x^2-1\\\\f'(x)=2x\ \ \ ,\ \ \ f'(0)=2\cdot 0=0\\\\\\\star \ \ f(x)=(x^2-1)\cdot cosx\\\\f'(x)=2x\cdot cosx+(x^2-1)\cdot sinx\\\\f'(0)=2\cdot 0\cdot 1+(0-1)\cdot 0=0+0=0\ \ \star$