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Beliebt Rechnen >

derivative of (ln(x)^7)

Lösung

\frac{d}{d x} ((ln (x))^{7})

Lösung

\frac{7 ln ^{6} ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} ((ln (x))^{7})

Wende die Kettenregel an:

7 (ln (x))^{6} \frac{d}{d x} (ln (x))

= 7 (ln (x))^{6} \frac{d}{d x} (ln (x))

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 7 (ln (x))^{6} \frac{1}{x}

Vereinfache

7 ln^{6} (x) \frac{1}{x} : \frac{7 ln ^{6} ( x )}{x}

= \frac{7 ln ^{6} ( x )}{x}

Graph

Beliebte Beispiele

derivative y=sqrt(13-x^9)

d er i v a t i v e y = 13 - x^{9}

(\partial)/(\partial x)(6x^2e^y-7xy^3)

\frac{\partial}{\partial x} (6 x^{2} e^{y} - 7 x y^{3})

integral of ((1+cot^2(z))cot(z))/(csc(z))

\int \frac{( 1 + cot ^{2} ( z ) ) cot ( z )}{csc ( z )} d z

integral of ze^y

\int z e^{y} d y

(dy)/(dt)=1+t+y+ty

\frac{d y}{d t} = 1 + t + y + t y