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Beliebt Rechnen >

derivative of 4x^4ln(x)

Lösung

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

Lösung

4 (4 x^{3} ln (x) + x^{3})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{4}, g = ln (x)

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 (4 x^{3} ln (x) + \frac{1}{x} x^{4})

\frac{1}{x} x^{4} = x^{3}

= 4 (4 x^{3} ln (x) + x^{3})

Graph

Beliebte Beispiele

y^{^{'}} = x - x^{2}

tangent y=x^3-9x,(3,0)

t an g e n t y = x^{3} - 9 x, (3, 0)

f (x) = x - 5

limit as x approaches infinity of-3/x

x \to \infty lim (- \frac{3}{x})

y^'+3(tan(3x))y=-2cos(3x)

y^{^{'}} + 3 (tan (3 x)) y = - 2 cos (3 x)