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Beliebt Rechnen >

derivative 4x^5ln(x)

Lösung

ableitung von

4 x^{5} ln (x)

Lösung

4 (5 x^{4} ln (x) + x^{4})

Schritte zur Lösung

\frac{d}{d x} (4 x^{5} ln (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{5} ln (x))

Wende die Produktregel an:

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

f = x^{5}, g = ln (x)

= 4 (\frac{d}{d x} (x^{5}) ln (x) + \frac{d}{d x} (ln (x)) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 4 (5 x^{4} ln (x) + \frac{1}{x} x^{5})

\frac{1}{x} x^{5} = x^{4}

= 4 (5 x^{4} ln (x) + x^{4})

Graph

Beliebte Beispiele

derivative of 3-4x

\frac{d}{d x} (3 - 4 x)

laplacetransform-4

l a pl a ce t r an s f or m - 4

f(x)=e^{x^2-4}+2x+9

f (x) = e^{x^{2} - 4} + 2 x + 9

integral of e^{i8x}cos(3x)

\int e^{i 8 x} cos (3 x) d x

integral from 1 to 2 of (x/2-2/x)

\int_{1}^{2} (\frac{x}{2} - \frac{2}{x}) d x