derivative of 1/(\sqrt[3]{(6x^2+5^2)})

Lösung

\frac{d}{d x} \frac{1}{3 ( 6 x ^{2} + 5 ) ^{2}}

- \frac{8 x}{( 6 x ^{2} + 5 ) ^{\frac{5}{3}}}

Schritte zur Lösung

\frac{d}{d x} \frac{1}{3 ( 6 x ^{2} + 5 ) ^{2}}

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} (((6 x^{2} + 5)^{2})^{- \frac{1}{3}})

Wende die Kettenregel an:

- \frac{1}{3 ( ( 6 x ^{2} + 5 ) ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} ((6 x^{2} + 5)^{2})

= - \frac{1}{3 ( ( 6 x ^{2} + 5 ) ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} ((6 x^{2} + 5)^{2})

\frac{d}{d x} ((6 x^{2} + 5)^{2}) = 24 x (6 x^{2} + 5)

= - \frac{1}{3 ( ( 6 x ^{2} + 5 ) ^{2} ) ^{\frac{4}{3}}} \cdot 24 x (6 x^{2} + 5)

Vereinfache

- \frac{1}{3 ( ( 6 x ^{2} + 5 ) ^{2} ) ^{\frac{4}{3}}} \cdot 24 x (6 x^{2} + 5) : - \frac{8 x}{( 6 x ^{2} + 5 ) ^{\frac{5}{3}}}

= - \frac{8 x}{( 6 x ^{2} + 5 ) ^{\frac{5}{3}}}

\int \frac{k}{x ln ( x )} d x

\frac{d}{d x} (\frac{x}{x ^{2} - 8})

\frac{d}{d x} (y z e^{x})

\frac{d y}{d x} = x y + 2 x + 3 y + 6

t an g e n t 7 x^{2}, at x = 10