Найдите производную

1) f (x) = 1 / |x| f (-2) = ?

2) f (x) = (x+4) ^2 / x-3

3) f (x) = x^2-2 / x^2 + 2 f' (2) = ?

Решение

1) f (x) = 1 / |x| f (-2) = ?

f' (x) = - 1/x²; f (-2) = 1/2

2) f (x) = (x+4) ^2 / (x-3)

f' (x) = [2 * (x+4) * (x - 3) - (x+4) ²]/x²

3) f (x) = (x^2-2) / (x^2 + 2) f' (2) = ?

f' (x) = [2x * (x²+2) - 2x * (x² - 2]/x⁴ = 8x / x⁴ = 8/x³

f' (2) = 8 / 2³ = 1