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Beliebt Rechnen >

derivative of (ln(2x+1)^{1/2})

Lösung

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

Lösung

\frac{1}{ln ^{\frac{1}{2}} ( 2 x + 1 ) ( 2 x + 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{2 ln ^{\frac{1}{2}} ( 2 x + 1 )} \cdot \frac{2}{2 x + 1}

Vereinfache

\frac{1}{2 ln ^{\frac{1}{2}} ( 2 x + 1 )} \cdot \frac{2}{2 x + 1} : \frac{1}{ln ^{\frac{1}{2}} ( 2 x + 1 ) ( 2 x + 1 )}

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

Graph

Beliebte Beispiele

integral of tan^2(2x)sec^2(2x)

\int tan^{2} (2 x) sec^{2} (2 x) d x

derivative of 3x-5sqrt(x)

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

integral of x(x+7)^4

\int x (x + 7)^{4} d x

(1+x^2)(dy)/(dx)-xy=0

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

limit as t approaches a of ln(t)

t \to a lim (ln (t))