derivative of \sqrt[3]{9x^2+7}

Lösung

\frac{d}{d x} (3 9 x^{2} + 7)

\frac{6 x}{( 9 x ^{2} + 7 ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (3 9 x^{2} + 7)

Wende die Kettenregel an:

\frac{1}{3 ( 9 x ^{2} + 7 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x^{2} + 7)

= \frac{1}{3 ( 9 x ^{2} + 7 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x^{2} + 7)

\frac{d}{d x} (9 x^{2} + 7) = 18 x

= \frac{1}{3 ( 9 x ^{2} + 7 ) ^{\frac{2}{3}}} \cdot 18 x

Vereinfache

\frac{1}{3 ( 9 x ^{2} + 7 ) ^{\frac{2}{3}}} \cdot 18 x : \frac{6 x}{( 9 x ^{2} + 7 ) ^{\frac{2}{3}}}

= \frac{6 x}{( 9 x ^{2} + 7 ) ^{\frac{2}{3}}}

t an g e n t f (x) = 4 cos (x), (\frac{π}{3}, 2)

\frac{\partial}{\partial w} (t e^{\frac{w}{t}})

\int \frac{x e ^{3 x}}{2} d x

\int_{k}^{2 k} \frac{2}{( 2 x - k ) ^{2}} d x

\int \frac{sec ( x )}{sec ( x ) - cos ( x )} d x