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Beliebt Rechnen >

derivative f(x)=(ln(x^5))^2

Lösung

ableitung von

f (x) = (ln (x^{5}))^{2}

Lösung

\frac{10 ln ( x ^{5} )}{x}

Schritte zur Lösung

\frac{d}{d x} ((ln (x^{5}))^{2})

Wende die Kettenregel an:

2 ln (x^{5}) \frac{d}{d x} (ln (x^{5}))

= 2 ln (x^{5}) \frac{d}{d x} (ln (x^{5}))

\frac{d}{d x} (ln (x^{5})) = \frac{5}{x}

= 2 ln (x^{5}) \frac{5}{x}

Vereinfache

2 ln (x^{5}) \frac{5}{x} : \frac{10 ln ( x ^{5} )}{x}

= \frac{10 ln ( x ^{5} )}{x}

Graph

Beliebte Beispiele

integral of 9/(x^{-1)+3}

\int \frac{9}{x ^{- 1} + 3} d x

(\partial)/(\partial x)(ycos(x^2y))

\frac{\partial}{\partial x} (y cos (x^{2} y))

steigung (8 1/7 ,9),(4,3 1/5)

s l o p e (8 \frac{1}{7}, 9), (4, 3 \frac{1}{5})

tangent y=ln(x^2-5x+1),(5,0)

t an g e n t y = ln (x^{2} - 5 x + 1), (5, 0)

integral from 0 to pi/3 of xsin(6x)

\int_{0}^{\frac{π}{3}} x sin (6 x) d x