используя определение производной, найти производную функции: f (x)=2x-3x^2. На ...

June 2022 1 8 Report

используя определение производной, найти производную функции: f (x)=2x-3x^2. На фото пример решения

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kmike21

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$\frac{2(x+h)-3(x+h)^2-2x+3x^2}{h}=\frac{2x+2h-3(x^2+2hx+h^2)-2x+3x^2}{h}= \\ =\frac{2h-3x^2-6hx-3h^2+3x^2}{h}=\frac{2h-6hx-3h^2}{h}$
$f'(x)=\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}= \lim_{h \to 0} \frac{2h-6hx-3h^2}{h}= 2-6x-\lim_{h \to 0}3h =2-6x 
$
ответ: f'(x)=2-6x

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ldasha3012 August 2022 | 0 Ответы

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