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...

Question

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)=?

Answer 1

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