derivative of (x^{1/3}-1^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x y^{^{'}} = y + 3 x^{2} sin (x), y (π) = 0

\int_{2}^{4} \frac{1}{x ^{2} - 25} d x

x \to 0 lim ((4 x)^{7 x})

a re a - 2 x^{2} + x, - 2, 1

n = 0 \sum \infty \frac{1}{2}