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Beliebt Rechnen >

derivative of x^n(ln(x)^2)

Lösung

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

Lösung

n x^{n - 1} ln^{2} (x) + 2 x^{n - 1} ln (x)

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{n}, g = (ln (x))^{2}

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

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

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

= n x^{n - 1} (ln (x))^{2} + \frac{2 ln ( x )}{x} x^{n}

\frac{2 ln ( x )}{x} x^{n} = 2 x^{n - 1} ln (x)

= n x^{n - 1} ln^{2} (x) + 2 x^{n - 1} ln (x)

Graph

Beliebte Beispiele

derivative f(x)=(9-xe^x)/(x+e^x)

d er i v a t i v e f (x) = \frac{9 - x e ^{x}}{x + e ^{x}}

derivative of (5x-2^3)

\frac{d}{d x} ((5 x - 2)^{3})

derivative of sin^2(pi-x)

\frac{d}{d x} (sin^{2} (π - x))

(dy)/(dt)=(3t^2+te^{-t}+1)/(2y-4)

\frac{d y}{d t} = \frac{3 t ^{2} + t e ^{- t} + 1}{2 y - 4}

integral of a/(x^2)

\int \frac{a}{x ^{2}} d x