Question

Найти производную второго порядка от заданной функции, у " = ?

y = (x^2 + 3)ln(x - 3)

Answer 1

y = (x² + 3)ln(x - 3)

 

у ' = (x² + 3)' * ln(x - 3) + (x² + 3) * (ln(x - 3)) ' = 2x*ln(x - 3) + (x² + 3) * 1/(x-3) = 2x*ln(x - 3) + (x² + 3)/(x-3)

 

 

y" = 2*ln(x - 3) + 2x * 1/(x-3) + ((2x*(x-3) - 1*(x² + 3)))/(x-3)² = 2*ln(x - 3) + 2x /(x-3) + (2x²-6x -x² - 3)/(x-3)² = 2*ln(x - 3) + 2x /(x-3) + (x²-6x -3)/(x-3)²