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Beliebt Rechnen >

derivative ln(x^3)

Lösung

ableitung von

ln (x^{3})

Lösung

\frac{3}{x}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{3}))

Wende die Kettenregel an:

\frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

= \frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{1}{x ^{3}} \cdot 3 x^{2}

Vereinfache

\frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{3}{x}

= \frac{3}{x}

Graph

Beliebte Beispiele

derivative of ax^3+bx^2-c/3 x+d

\frac{d}{d x} (a x^{3} + b x^{2} - \frac{c}{3} x + d)

derivative y=x^2(x-1)

d er i v a t i v e y = x^{2} (x - 1)

(\partial)/(\partial x)(x^7y^9-x^6y^8)

\frac{\partial}{\partial x} (x^{7} y^{9} - x^{6} y^{8})

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

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

taylor (-5x+24)^{3/2}

t a y l or (- 5 x + 24)^{\frac{3}{2}}