(x^3+3x) 5) f(x)= 3cosx+2...

200600 @200600

July 2022 1 2 Report

Найти производную функции:
1)f(x) = 3x-5x^2 -x^3
2) f(x)= 1/3x - 4/x^3+ корень из х
3)f(x)=x^3(3x+x^3)
4) f(x)= 3x/ (x^3+3x)
5) f(x)= 3cosx+2

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NNNLLL54

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$1)\; \; f(x)=3x-5x^2-x^3\\\\f'(x)=3-10x-3x^2\\\\2)\; \; f(x)=\frac{1}{3x}-\frac{4}{x^3}+\sqrt{x}\\\\f'(x)=-\frac{3}{9x^2}+\frac{4\cdot 3x^2}{x^6}+\frac{1}{2\sqrt{x}}=-\frac{1}{3x^2}+\frac{12}{x^4}+\frac{1}{2\sqrt{x}}\\\\3)\; \; f(x)=x^3(3x+x^3)=3x^4+x^6\\\\f'(x)=12x^3+6x^5$

$4)\; \; f(x)=\frac{3x}{x^3+3x}\\\\f'(x)= \frac{3(x^3+3x)-3x(3x^2+3)}{(x^3+3x)^2} \\\\5)\; \; f(x)=3cosx+2\\\\f'(x)=-3sinx$

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