derivative of \sqrt[3]{1-x^2}

Lösung

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

- \frac{2 x}{3 ( 1 - x ^{2} ) ^{\frac{2}{3}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{3 ( 1 - x ^{2} ) ^{\frac{2}{3}}} (- 2 x)

Vereinfache

\frac{1}{3 ( 1 - x ^{2} ) ^{\frac{2}{3}}} (- 2 x) : - \frac{2 x}{3 ( 1 - x ^{2} ) ^{\frac{2}{3}}}

= - \frac{2 x}{3 ( 1 - x ^{2} ) ^{\frac{2}{3}}}

t an g e n t f (x) = x, at x = 25

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

\int \frac{2 x + 4}{x ^{2} + 4 x + 13} d x

n = 0 \sum \infty 1400700

n = 1 \sum \infty (\frac{5}{n})^{4}