Question

Помогите найти производную. пожалуйста ;) y=(x^2+7x-1)log3 x

Answer 1

$y=( x^{2} +7x-1) log_{3}x \ y'=( x^{2} +7x-1)' log_{3}x +( x^{2} +7x-1) (log_{3}x)'= \ = (2x+7) log_{3}x +( x^{2} +7x-1) frac{1}{x ln3 } = \ =2xlog_{3}x+7 log_{3}x + frac{x^{2} +7x-1}{x ln3 }$

Answer 2

y = log(3) x (x^2+7 x-1)
x log(3) (x^2+7 x-1) = x x^2 log(3)+x (7 x) log(3)+x (-1) log(3):
y = log(3) x x^2+7 log(3) x x-log(3) x
x×7 x log(3) = x^2×7 log(3):
y = log(3) x x^2+7 x^2 log(3)-log(3) x
x x^2 log(3) = x^(1+2) log(3):
y = x^3 log(3)+7 log(3) x^2-log(3) x
1+2 = 3:

| y = log(3) x^3+7 log(3) x^2-log(3) x