derivative of \sqrt[5]{2-x^2}

Lösung

\frac{d}{d x} (5 2 - x^{2})

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

Schritte zur Lösung

\frac{d}{d x} (5 2 - x^{2})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

t a y l or e^{x^{2} + x}

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

s im pl i f y e^{l n (s i n (x^{2}))} 2 x + 1

x \to 0 lim (\frac{ln ( x + 1 )}{x})

\int cos^{2} (10 x) d x