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Beliebt Rechnen >

derivative of ln((ax^n))

Lösung

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

Lösung

\frac{n}{x}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{( a x ) ^{n}} \frac{d}{d x} ((a x)^{n})

= \frac{1}{( a x ) ^{n}} \frac{d}{d x} ((a x)^{n})

\frac{d}{d x} ((a x)^{n}) = n a^{n} x^{n - 1}

= \frac{1}{( a x ) ^{n}} n a^{n} x^{n - 1}

Vereinfache

\frac{1}{( a x ) ^{n}} n a^{n} x^{n - 1} : \frac{n}{x}

= \frac{n}{x}

Graph

Beliebte Beispiele

(dy)/(dx)=y(1-y),y(0)=8

\frac{d y}{d x} = y (1 - y), y (0) = 8

limit as x approaches 4-of 3x-5

x \to 4 - lim (3 x - 5)

derivative 4x^3-56x^2+196x

d er i v a t i v e 4 x^{3} - 56 x^{2} + 196 x

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

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

integral of 2x^3e^{-2x}

\int 2 x^{3} e^{- 2 x} d x