derivative of \sqrt[3]{1+x^4}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (lo g_{4} (2 x + 3))

d er i v a t i v e f (x) = (5 t^{2} - 2 t + 1)^{\frac{3}{2}}

\int_{1}^{2} \frac{1}{( x + 1 ) ^{2}} d x

d er i v a t i v e f (x) = ∣ x - 1 ∣

\frac{\partial}{\partial y} (ln (x + 3 y))