derivative y=ln(sqrt(x^2+4))

Lösung

ableitung von

y = ln (x^{2} + 4)

\frac{x}{x ^{2} + 4}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} + 4))

Wende die Kettenregel an:

\frac{1}{x ^{2} + 4} \frac{d}{d x} (x^{2} + 4)

= \frac{1}{x ^{2} + 4} \frac{d}{d x} (x^{2} + 4)

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

= \frac{1}{x ^{2} + 4} \cdot \frac{x}{x ^{2} + 4}

Vereinfache

\frac{1}{x ^{2} + 4} \cdot \frac{x}{x ^{2} + 4} : \frac{x}{x ^{2} + 4}

= \frac{x}{x ^{2} + 4}

x \to 6 lim (x)

\int_{0}^{3 π^{2}} θ cos^{2} (θ^{\frac{3}{2}}) d θ

\frac{\partial}{\partial x} (\frac{2}{x} - x)

\frac{d}{d x} (- 8 e^{- 2 x})

x \to 4 lim (2 \cdot e^{\frac{2}{x - 4}})