найдите f`(x), если f(x) = (x^2-2)(x+3)...

July 2022 1 8 Report

найдите f`(x), если f(x) = (x^2-2)(x+3)

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nafanya2014

Verified answer

По формуле производная частного ( дроби):
$(\frac{u}{v})`= \frac{u`\cdot v- u \cdot v`}{v ^{2} }$

$(\frac{ x^{2} -2}{x+3})`= \frac{( x^{2} -2)`\cdot (x+3)- ( x^{2} -2) \cdot (x+3)`}{(x+3) ^{2} }=$

$=\frac{( 2x)\cdot (x+3)- ( x^{2} -2) \cdot 1}{(x+3) ^{2} }= \frac{2 x^{2} +6x- x^{2} +2}{(x+3) ^{2} }= \frac{ x^{2} +6x+2}{(x+3) ^{2} }$

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