derivative ln(sqrt(x^2))

Lösung

ableitung von

ln (x^{2})

\frac{x}{x ^{2} ∣ x ∣}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{2}) = \frac{x}{∣ x ∣}

= \frac{1}{x ^{2}} \cdot \frac{x}{∣ x ∣}

Vereinfache

\frac{1}{x ^{2}} \cdot \frac{x}{∣ x ∣} : \frac{x}{x ^{2} ∣ x ∣}

= \frac{x}{x ^{2} ∣ x ∣}

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

\frac{d}{d x} (3 x^{5} - 5 x^{3} - 10)

d er i v a t i v e (4 t - 1) (3 t - 6)^{- 1}

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 1

\frac{\partial}{\partial y} (8 x^{\frac{y}{z}})