derivative \sqrt[3]{5+9x^2}

Lösung

ableitung von

3 5 + 9 x^{2}

\frac{6 x}{( 5 + 9 x ^{2} ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (3 5 + 9 x^{2})

Wende die Kettenregel an:

\frac{1}{3 ( 5 + 9 x ^{2} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 9 x^{2})

= \frac{1}{3 ( 5 + 9 x ^{2} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 9 x^{2})

\frac{d}{d x} (5 + 9 x^{2}) = 18 x

= \frac{1}{3 ( 5 + 9 x ^{2} ) ^{\frac{2}{3}}} \cdot 18 x

Vereinfache

\frac{1}{3 ( 5 + 9 x ^{2} ) ^{\frac{2}{3}}} \cdot 18 x : \frac{6 x}{( 5 + 9 x ^{2} ) ^{\frac{2}{3}}}

= \frac{6 x}{( 5 + 9 x ^{2} ) ^{\frac{2}{3}}}

x \to 5 lim (ln (x - 5))

\frac{d}{d x} (e + L (x))

d er i v a t i v e \frac{x ^{3}}{4}

s l o p e y^{3} - x y^{2} = 4

d er i v a t i v e y = \frac{3}{x + 7}