Question

найти производную функции

y=(x+9)^2(x+3)+7

 

Answer 1

y = (x + 9)^2 (x + 3) + 7 

y ' = ((x + 9)^2*(x + 3) )' =  ((x + 9)^2)'(x + 3) + (x + 3)'(x  + 9)^2 =
= 2 (x + 9)(x + 3) + (x + 9)^2 =
= 2 (x^2 + 12x + 27) + x^2 + 18x + 81 = 
= 2x^2 + 24x + 54 + x^2 + 18x + 81 = 
= 3x^2 + 42x + 135 = 3(x^2 + 14x+ 45)