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

Lösung

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

10 (3 x^{2} g (x) + \frac{d}{d x} (g (x)) x^{3}) - \frac{4}{x ^{3}}

Schritte zur Lösung

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

Vereinfache

5 g (x) (2 x^{3}) + \frac{2}{x ^{2}} : 10 x^{3} g (x) + \frac{2}{x ^{2}}

= \frac{d}{d x} (10 x^{3} g (x) + \frac{2}{x ^{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (10 x^{3} g (x)) + \frac{d}{d x} (\frac{2}{x ^{2}})

\frac{d}{d x} (10 x^{3} g (x)) = 10 (3 x^{2} g (x) + \frac{d}{d x} (g (x)) x^{3})

\frac{d}{d x} (\frac{2}{x ^{2}}) = - \frac{4}{x ^{3}}

= 10 (3 x^{2} g (x) + \frac{d}{d x} (g (x)) x^{3}) - \frac{4}{x ^{3}}

\int_{0}^{3} e^{- 2 x} d x

\frac{\partial}{\partial x} (2 x y e^{- x^{2} y})

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

\int sin^{2} (9 x) cos^{2} (9 x) d x

\int \frac{4}{15} x^{\frac{5}{2}} + 6 cos (x) + C x + D d x