derivative of ln(6x^3+3x^2-2x)

Lösung

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

\frac{18 x ^{2} + 6 x - 2}{6 x ^{3} + 3 x ^{2} - 2 x}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{6 x ^{3} + 3 x ^{2} - 2 x} \frac{d}{d x} (6 x^{3} + 3 x^{2} - 2 x)

= \frac{1}{6 x ^{3} + 3 x ^{2} - 2 x} \frac{d}{d x} (6 x^{3} + 3 x^{2} - 2 x)

\frac{d}{d x} (6 x^{3} + 3 x^{2} - 2 x) = 18 x^{2} + 6 x - 2

= \frac{1}{6 x ^{3} + 3 x ^{2} - 2 x} (18 x^{2} + 6 x - 2)

Vereinfache

\frac{1}{6 x ^{3} + 3 x ^{2} - 2 x} (18 x^{2} + 6 x - 2) : \frac{18 x ^{2} + 6 x - 2}{6 x ^{3} + 3 x ^{2} - 2 x}

= \frac{18 x ^{2} + 6 x - 2}{6 x ^{3} + 3 x ^{2} - 2 x}

t an g e n t f (x) = x + 2, at (x = 4)

\int 2 y e^{y^{2}} d y

\int x^{2} (x^{2} + 1) d x

\frac{d y}{d x} + y \cdot 1 + x^{2} = 0

\frac{d y}{d x} = \frac{x}{( 1 + 2 y )}, y (- 1) = 0