derivative (2ra^{rx}+n)^p

Lösung

ableitung von

(2 r a^{r x} + n)^{p}

p (2 r a^{r x} + n)^{p - 1} \cdot 2 (x a^{x r} r ln (a) + a^{x r})

Schritte zur Lösung

\frac{d}{d r} ((2 r a^{r x} + n)^{p})

Behandle

a, n, x, p

als Konstanten

Wende die Kettenregel an:

p (2 r a^{r x} + n)^{p - 1} \frac{d}{d r} (2 r a^{r x} + n)

= p (2 r a^{r x} + n)^{p - 1} \frac{d}{d r} (2 r a^{r x} + n)

\frac{d}{d r} (2 r a^{r x} + n) = 2 (x a^{x r} r ln (a) + a^{x r})

= p (2 r a^{r x} + n)^{p - 1} \cdot 2 (x a^{x r} r ln (a) + a^{x r})

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