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Beliebt Rechnen >

derivative of x^v

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

Beliebte Beispiele

integral of (1+x+x^2)/(sqrt(x))

\int \frac{1 + x + x ^{2}}{x} d x

integral of (ln(x))/(x^a)

\int \frac{ln ( x )}{x ^{a}} d x

integral of ((3x^2+2))/(x-1)

\int \frac{( 3 x ^{2} + 2 )}{x - 1} d x

integral of sin(3x)sin(kx)

\int sin (3 x) sin (k x) d x

integral of (3x-4)^7

\int (3 x - 4)^{7} d x