derivative of (2x^6+5x^3^{3/5})

Lösung

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

\frac{3 ( 12 x ^{5} + 15 x ^{2} )}{5 ( 2 x ^{6} + 5 x ^{3} ) ^{\frac{2}{5}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x^{6} + 5 x^{3}) = 12 x^{5} + 15 x^{2}

= \frac{3}{5 ( 2 x ^{6} + 5 x ^{3} ) ^{\frac{2}{5}}} (12 x^{5} + 15 x^{2})

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( 12 x ^{5} + 15 x ^{2} )}{5 ( 2 x ^{6} + 5 x ^{3} ) ^{\frac{2}{5}}}

n = 1 \sum \infty 1 + (\frac{1}{2})^{n}

x^{2} y^{^{''}} - 3 x y^{^{'}} + 4 y = x

x \to - \infty lim (\frac{7}{x} - 2)

x \to 0 lim (\frac{1}{cos ( x ) - 1})

\frac{d}{d x} (3 x^{4})