derivative of sqrt((4-x^{2/3)^3})

Lösung

\frac{d}{d x} ((4 - x^{\frac{2}{3}})^{3})

- \frac{( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} ((4 - x^{\frac{2}{3}})^{3})

Wende die Kettenregel an:

\frac{1}{2 ( ( 4 - x ^{\frac{2}{3}} ) ^{3} ) ^{\frac{1}{2}}} \frac{d}{d x} ((4 - x^{\frac{2}{3}})^{3})

= \frac{1}{2 ( ( 4 - x ^{\frac{2}{3}} ) ^{3} ) ^{\frac{1}{2}}} \frac{d}{d x} ((4 - x^{\frac{2}{3}})^{3})

\frac{d}{d x} ((4 - x^{\frac{2}{3}})^{3}) = - \frac{2 ( 4 - x ^{\frac{2}{3}} ) ^{2}}{x ^{\frac{1}{3}}}

= \frac{1}{2 ( ( 4 - x ^{\frac{2}{3}} ) ^{3} ) ^{\frac{1}{2}}} - \frac{2 ( 4 - x ^{\frac{2}{3}} ) ^{2}}{x ^{\frac{1}{3}}}

Vereinfache

\frac{1}{2 ( ( 4 - x ^{\frac{2}{3}} ) ^{3} ) ^{\frac{1}{2}}} - \frac{2 ( 4 - x ^{\frac{2}{3}} ) ^{2}}{x ^{\frac{1}{3}}} : - \frac{( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

= - \frac{( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

x \to - 8 lim (1 + - 2 x)

\frac{\partial}{\partial x} (x - 2)

\int y sin (x + y^{2}) d y

y^{^{'}} = 3 y t

x \to 0 + lim (\frac{sin ( 2 x )}{x})