derivative of \sqrt[3]{x^2-4}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int sec^{6} (4 x) tan (4 x) d x

a re a f (x) = x^{2}, 0, 4

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (1) = e^{2}, y^{^{'}} (1) = 3 e^{2}

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

x \to π lim (sin (x - π))