derivative f(x)=\sqrt[3]{x^5}

Lösung

ableitung von

f (x) = 3 x^{5}

\frac{5 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (3 x^{5})

Wende die Kettenregel an:

\frac{1}{3 ( x ^{5} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{5})

= \frac{1}{3 ( x ^{5} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{1}{3 ( x ^{5} ) ^{\frac{2}{3}}} \cdot 5 x^{4}

Vereinfache

\frac{1}{3 ( x ^{5} ) ^{\frac{2}{3}}} \cdot 5 x^{4} : \frac{5 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

= \frac{5 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

d er i v a t i v e y = \frac{1}{2 x - 1}

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

\frac{d}{d x} (arccos (2 x^{2}))

\int 2 + t^{2} d t

\int \frac{8}{x ^{2} x ^{2} + 25} d x