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Beliebt Rechnen >

derivative 7(3x^2ln(5x)+x^2)

Lösung

ableitung von

7 (3 x^{2} ln (5 x) + x^{2})

Lösung

7 (6 x ln (5 x) + 5 x)

Schritte zur Lösung

\frac{d}{d x} (7 (3 x^{2} ln (5 x) + x^{2}))

Entferne die Konstante:

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

= 7 \frac{d}{d x} (3 x^{2} ln (5 x) + x^{2})

Wende die Summen-/Differenzregel an:

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

= 7 (\frac{d}{d x} (3 x^{2} ln (5 x)) + \frac{d}{d x} (x^{2}))

\frac{d}{d x} (3 x^{2} ln (5 x)) = 3 (2 x ln (5 x) + x)

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

= 7 (3 (2 x ln (5 x) + x) + 2 x)

Multipliziere aus

3 (2 x ln (5 x) + x) + 2 x : 6 x ln (5 x) + 5 x

= 7 (6 x ln (5 x) + 5 x)

Graph

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