derivative of (2x+5^{1/3})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x + 5) = 2

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

Vereinfache

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

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

d er i v a t i v e 5 t - 5 e^{t}

\int (\frac{3}{x} + 3 x) d x

\frac{d}{d x} (x (cos (x)))

d er i v a t i v e 9 x^{2} - 1

d er i v a t i v e y = cos^{4} (t) - sin^{4} (t)