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Beliebt Rechnen >

derivative of x^r

Lösung

\frac{d}{d x} (x^{r (x)})

Lösung

x^{r} (ln (x) \frac{d r}{d x} + \frac{r}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{r})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{r} = e^{r l n (x)}

= \frac{d}{d x} (e^{r l n (x)})

Wende die Kettenregel an:

e^{r l n (x)} \frac{d}{d x} (r ln (x))

= e^{r l n (x)} \frac{d}{d x} (r ln (x))

\frac{d}{d x} (r ln (x)) = ln (x) \frac{d r}{d x} + \frac{r}{x}

= e^{r l n (x)} (ln (x) \frac{d r}{d x} + \frac{r}{x})

e^{r l n (x)} = x^{r}

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

Beliebte Beispiele

vereinfachen 2cos(x^3)-2/x

normal y=4x-1,(1,-4)

(\partial)/(\partial x)(4xsin(xy))

(\partial)/(\partial x)(3x^2+xy+y^2-8)

derivative of log_{e}(3x)