find the derivative of the following functions:
(i) f(x) = −x 2 + 10x + 4
(ii) f(x) = 20 − 1 x+2
(iii) f(x) = x 4 e −2x 2
(iv) f(x) = ln(x 2 + 2x + 2).
using the differentiation rules : derivative definition and operation rules (sum, subtraction, multiplication, quotient), derivative of many basic functions (power, quadratic, exponential and natural logarithm functions), function of functions: (chain rule).
explain carefully what rule(s) you have used and where you have applied it(them)