Question

Знайти похідну функції f(x) = (cos⁡(π+x))/(cos⁡(π/2+x)) в точці x0 = -π/4

Answer 1

$\huge \sf f(x)=\frac{cos(\pi+x)}{cos(\frac{\pi}{2}+x)}\\\\f(x)=\frac{-cos(x)}{-sin(x)}=ctg(x)\\\\f'(x)=-\frac{1}{sin^2(x)} \\\\f'(x_0)=-\frac{1}{sin^2(\frac{-\pi}{4} )}=-2$