Übung
$\frac{d^2}{dx^2}\left(x^{n-1}\log\left(x\right)\right)$
Schritt-für-Schritt-Lösung
Zwischenschritte
1
Ermitteln Sie die Ableitung ($1$)
$\left(n-1\right)x^{\left(n-2\right)}\log \left(x\right)+\frac{x^{\left(n-1\right)}}{\ln\left(10\right)x}$
Zwischenschritte
$\left(n-1\right)x^{\left(n-2\right)}\log \left(x\right)+\frac{x^{\left(n-2\right)}}{\ln\left(10\right)}$
Zwischenschritte
3
Ermitteln Sie die Ableitung ($2$)
$\frac{\left(n-1\right)\left(\frac{x^{\left(n-2\right)}}{x}+\left(n-2\right)x^{\left(n-3\right)}\ln\left(x\right)\right)}{\ln\left(10\right)}+\frac{\left(n-2\right)x^{\left(n-3\right)}}{\ln\left(10\right)}$
Zwischenschritte
$\frac{\left(n-1\right)\left(x^{\left(n-3\right)}+\left(n-2\right)x^{\left(n-3\right)}\ln\left(x\right)\right)+\left(n-2\right)x^{\left(n-3\right)}}{\ln\left(10\right)}$
Endgültige Antwort auf das Problem
$\frac{\left(n-1\right)\left(x^{\left(n-3\right)}+\left(n-2\right)x^{\left(n-3\right)}\ln\left(x\right)\right)+\left(n-2\right)x^{\left(n-3\right)}}{\ln\left(10\right)}$