Задача 57081 Найти производные следующих функций:...
Условие
Решение
[m]y`=4\cdot (7x^5-3\sqrt[3]{x^2}-6)^3\cdot (7x^5-3\sqrt[3]{x^2}-6)`[/m]
[m]y`=4\cdot (7x^5-3\sqrt[3]{x^2}-6)^3\cdot (35x^4-3\cdot \frac{2}{3}\cdot x^{\frac{2}{3}-1}-0)[/m]
[m]y`=4\cdot (7x^5-3\sqrt[3]{x^2}-6)^3\cdot (35x^4- \frac{2}{\sqrt[3]{x}})[/m]
c)
[m]y`=\frac{(3x)`}{\sqrt{1-(3x)^2}}-\frac{1}{2\sqrt{1-9x^2}}\cdot(1-9x^2)`[/m]
[m]y`=\frac{3}{\sqrt{1-9x^2}}+\frac{18x}{2\sqrt{1-9x^2}}[/m]
[m]y`=\frac{3+9x}{\sqrt{1-9x^2}}[/m]
d)
[m]y=\frac{2x+tg3x}{e^{2x}}[/m]
[m]y`=\frac{(2x+tg3x)`\cdot e^{2x}-(2x+tg3x)\cdot (e^{2x})`}{(e^{2x})^2}[/m]
[m]y`=\frac{(2+\frac{(3x)`}{cos^23x})\cdot e^{2x}-(2x+tg3x)\cdot (e^{2x})\cdot (2x)`}{e^{4x}}[/m]
[m]y`=\frac{(2+\frac{3}{cos^23x})\cdot e^{2x}-2(2x+tg3x)\cdot e^{2x}}{e^{4x}}[/m]
[m]y`=\frac{(2+\frac{3}{cos^23x}-4x-2tg3x)\cdot e^{2x}}{e^{4x}}[/m]
[m]y`=\frac{2+\frac{3}{cos^23x}-4x-2tg3x}{e^{2x}}[/m]
e)
[m]y`=5^{ctgx}\cdot ln5\cdot (ctgx)`-((\sqrt{x})`\cdot cos2x+\sqrt{x}\cdot (cos2x)`)[/m]
[m]y`=5^{ctgx}\cdot ln5\cdot(- \frac{1}{sin^2x})-((\frac{1}{2\sqrt{x}})\cdot cos2x+\sqrt{x}\cdot (-sin2x)\cdot (2x)`)[/m]
[m]y`=5^{ctgx}\cdot ln5\cdot(- \frac{1}{sin^2x})-((\frac{1}{2\sqrt{x}})\cdot cos2x+\sqrt{x}\cdot (-sin2x)\cdot 2)[/m]
[m]y`=- \frac{5^{ctgx}\cdot ln5}{sin^2x}-\frac{cos2x}{2\sqrt{x}}+2\sqrt{x}\cdot sin2x[/m]