derivative of \sqrt[13]{9+7\sqrt[5]{2x}}

Lösung

\frac{d}{d x} (13 9 + 7 5 2 x)

\frac{7 5 2}{65 x ^{\frac{4}{5}} ( 9 + 7 5 2 5 x ) ^{\frac{12}{13}}}

Schritte zur Lösung

\frac{d}{d x} (13 9 + 7 5 2 x)

Wende die Kettenregel an:

\frac{1}{13 ( 9 + 7 5 2 x ) ^{\frac{12}{13}}} \frac{d}{d x} (9 + 7 5 2 x)

= \frac{1}{13 ( 9 + 7 5 2 x ) ^{\frac{12}{13}}} \frac{d}{d x} (9 + 7 5 2 x)

\frac{d}{d x} (9 + 7 5 2 x) = \frac{7 5 2}{5 x ^{\frac{4}{5}}}

= \frac{1}{13 ( 9 + 7 5 2 x ) ^{\frac{12}{13}}} \cdot \frac{7 5 2}{5 x ^{\frac{4}{5}}}

Vereinfache

\frac{1}{13 ( 9 + 7 5 2 x ) ^{\frac{12}{13}}} \cdot \frac{7 5 2}{5 x ^{\frac{4}{5}}} : \frac{7 5 2}{65 x ^{\frac{4}{5}} ( 9 + 7 5 2 5 x ) ^{\frac{12}{13}}}

= \frac{7 5 2}{65 x ^{\frac{4}{5}} ( 9 + 7 5 2 5 x ) ^{\frac{12}{13}}}

\int (sec^{2} (θ) + sec (θ) tan (θ)) d θ

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

\frac{\partial}{\partial y} (2 - y - 2 x)

\frac{\partial}{\partial x} (x^{2} y sin (\frac{1}{x}))

x \to 0 lim (- x^{3})