Pochodne

[alicja403]

Oblicz pochodne funkcji
\(y= \frac{5}{ \sqrt[7]{x} } -2x^7+ \frac{3}{2 \sqrt{x} }\)
\(y=t \sqrt[3]{t}\)
\(y= \frac{2}{x^3 \sqrt{x} }\)

[irena]

1.
\(y=5x^{-\frac{1}{7}}-2x^7+\frac{3}{2}x^{-\frac{1}{2}}\\y'=-\frac{5}{7}x^{-\frac{8}{7}}-14x^6-\frac{3}{4}x^{-\frac{3}{2}}=-\frac{5}{7x\sqrt[7]{x}}-14x^6-\frac{3}{4x\sqrt{x}}\)

[irena]

2.
\(y=t\sqrt[3]{t}=t^{\frac{4}{3}}\\y'=\frac{4}{3}t^{\frac{1}{3}}=\frac{4\sqrt[3]{t}}{3}\)

[irena]

3.
\(y=2x^{-\frac{7}{2}}\\y'=-7x^{-\frac{9}{2}}=-\frac{7}{x^4\sqrt{x}}\)