derivative (5x^3+3x^2)/x

Lösung

ableitung von

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

10 x + 3

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 5 x + 3

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

\frac{d x}{d x} = 1

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

= 1 \cdot (5 x + 3) + 5 x

Vereinfache

= 10 x + 3

\frac{\partial}{\partial x} (x^{2} (1 - y^{\frac{2}{5}}))

d er i v a t i v e y = x + x^{\frac{3}{2}} - 8 x

(5 x^{3} + 3 x y + 2 y^{2}) d x + (x^{2} + 2 x y) d y = 0

\frac{d}{d x} (ln (x^{2} + 2 x))

x \to 0 lim (ln (2 x^{2} + x))