Вычислить производную функции.

а) f (x) = 3x (x³+5)

б) f (x) = x²/x⁴+1

в) f (x) = 2x^5-4x³+6x²-11

г) f (x) = (x³+3) ^7

A) f' (x) = (3x) ' (x^3+5) + (x^3+5) '•3x=

3x^3+15+9x^3=12x^3+15

2) f' (x) = (x^2 / (x^4+1)) ' = ((x^2) ' (x^4+1) - ((x^4+1) 'x^2) :

(x^4+1) ^2=

(2x^5+2x-4x^5) / ((x^4+1) ^2) = (2x-2x^5) / (x^4+1) ^2

3) f' (x) = 10x^4-12x^2+12x

4) f' (x) = ((x^3+3) ^7) '=7 (x^3+3) ^6 * (x^3+3) '=

21 (x^3+3) ^6*x^2