Найдите производную функции: a). [latex]y=x^2+x^3[/latex] b). [latex]y=x^7-x^3[/latex] c). [latex]y=4x^5-2[/latex] d). [latex]y=-5x^3+4[/latex] e). [latex]y=\frac{1}{x}(2x+1)[/latex] f). [latex]y=\frac{1}{x}(x^6-5)[/latex] g). ...

Question

Найдите производную функции: a). [latex]y=x^2+x^3[/latex] b). [latex]y=x^7-x^3[/latex] c). [latex]y=4x^5-2[/latex] d). [latex]y=-5x^3+4[/latex] e). [latex]y=\frac{1}{x}(2x+1)[/latex] f). [latex]y=\frac{1}{x}(x^6-5)[/latex] g). ...

Найдите производную функции: a). [latex]y=x^2+x^3[/latex] b). [latex]y=x^7-x^3[/latex] c). [latex]y=4x^5-2[/latex] d). [latex]y=-5x^3+4[/latex] e). [latex]y=\frac{1}{x}(2x+1)[/latex] f). [latex]y=\frac{1}{x}(x^6-5)[/latex] g). [latex]y=(1-x^{20})\frac{1}{x}[/latex] h). [latex]y=\frac{2}{x}[/latex] i). [latex]y=\frac{x-3}{x}[/latex] j). [latex] y=\frac{x+1}{\sqrt{x}}[/latex]

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Ответ(ы) на вопрос:

Accepted Answer

[latex]y=x^2+x^3;\\ y'=2x+3x^2;[/latex] [latex]y=x^7-x^3;\\ y'=7x^6-3x^2; [/latex] [latex]y=4x^5-2;\\ y'=20x^4;[/latex] [latex]y=-5x^3+4;\\ y'=-15x^2; [/latex] [latex]y=\frac{1}{x}(2x+1)=2+\frac{1}{x};\\ y'=-\frac{1}{x^2}[/latex] [latex]y=\frac{1}{x}(x^6-5)=x^5-\frac{5}{x};\\ y'=5x^4-\frac{5}{x^2}; [/latex] [latex]y=(1-x^{20})\frac{1}{x}=\frac{1}{x}-x^{19};\\ y'=-\frac{1}{x^2}-19x^{18}[/latex] [latex]y=\frac{2}{x};\\ y'=-\frac{2}{x^2}[/latex] [latex]y=\frac{x-3}{x}=1-\frac{3}{x};\\ y'=-\frac{3}{x^2}[/latex] [latex]y=\frac{x+1}{\sqrt{x}}=\sqrt{x}+x^{-\frac{1}{2}};\\ y'=\frac{1}{2\sqrt{x}}- \frac{1}{2x\sqrt{x}}[/latex]