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Beliebt Rechnen >

derivative of 5x^4ln(x+x^4)

Lösung

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

Lösung

20 x^{3} ln (x) + 9 x^{3}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (5 x^{4} ln (x)) = 5 (4 x^{3} ln (x) + x^{3})

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

= 5 (4 x^{3} ln (x) + x^{3}) + 4 x^{3}

Vereinfache

5 (4 x^{3} ln (x) + x^{3}) + 4 x^{3} : 20 x^{3} ln (x) + 9 x^{3}

= 20 x^{3} ln (x) + 9 x^{3}

Graph

Beliebte Beispiele

fläche 1/4 (x-3)^2+1,x^2+1,0,3

a re a \frac{1}{4} (x - 3)^{2} + 1, x^{2} + 1, 0, 3

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

(\partial)/(\partial x)(x^3+2xy)

\frac{\partial}{\partial x} (x^{3} + 2 x y)

fläche x^2-4,-4,3

a re a x^{2} - 4, - 4, 3

inverselaplace x/((x-1)^2)

in v erse l a pl a ce \frac{x}{( x - 1 ) ^{2}}