task/27168089
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Найти производную функции y=(x² + 7)/9x
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* * * (u/v) ' =(u ' *v -u*v ') /v² * * *
y '= ( (x² + 7)/9x ) ' =(1/9) *( (x² + 7) ' *x -(x² + 7)* (x) ' ) /x² =
(1/9) *( (2x+0)*x -(x² + 7)* 1 ) / x² =(1/9) *( 2x² -x² - 7) /x² =(x² - 7) / 9x² .
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y '= ( (x² + 7)/9x ) ' =( (x² + 7)' *9x -(x² + 7) *(9x) ' ) / (9x)² =
( (2x + 0)*9x -(x² + 7) *9 ) / (81x²) =(9x² - 63)/ (81x²) =9(x² - 7) / (81x²) =
=(x² - 7) / 9x².