derivative of \sqrt[3]{x^2}+2sqrt(x^5)

Lösung

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

\frac{2 + 15 x ^{\frac{11}{6}}}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{2}{3 x ^{\frac{1}{3}}} + 5 x^{\frac{3}{2}}

Vereinfache

\frac{2}{3 x ^{\frac{1}{3}}} + 5 x^{\frac{3}{2}} : \frac{2 + 15 x ^{\frac{11}{6}}}{3 x ^{\frac{1}{3}}}

= \frac{2 + 15 x ^{\frac{11}{6}}}{3 x ^{\frac{1}{3}}}

x \to \infty lim (\frac{3 x ^{2} + 10 x - 7}{2 x ^{2} - 5 x})

y^{^{''}} - 6 y^{^{'}} + 25 y = - 45 cos (2 t) + 30 sin (2 t)

\frac{d}{d x} (ln (coth (x)))

\int \frac{cos ( 5 x )}{e ^{s i n (5 x)}} d x

\frac{d y}{d x} = 9 x + y