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Beliebt Rechnen >

derivative of (5x^2-3*(x^2+x+4))

Lösung

\frac{d}{d x} ((5 x^{2} - 3) \cdot (x^{2} + x + 4))

Lösung

20 x^{3} + 15 x^{2} + 34 x - 3

Schritte zur Lösung

\frac{d}{d x} ((5 x^{2} - 3) (x^{2} + x + 4))

Wende die Produktregel an:

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

f = 5 x^{2} - 3, g = x^{2} + x + 4

= \frac{d}{d x} (5 x^{2} - 3) (x^{2} + x + 4) + \frac{d}{d x} (x^{2} + x + 4) (5 x^{2} - 3)

\frac{d}{d x} (5 x^{2} - 3) = 10 x

\frac{d}{d x} (x^{2} + x + 4) = 2 x + 1

= 10 x (x^{2} + x + 4) + (2 x + 1) (5 x^{2} - 3)

Vereinfache

10 x (x^{2} + x + 4) + (2 x + 1) (5 x^{2} - 3) : 20 x^{3} + 15 x^{2} + 34 x - 3

= 20 x^{3} + 15 x^{2} + 34 x - 3

Graph

Beliebte Beispiele

derivative of e^x(12x^2-24x+24)

\frac{d}{d x} (e^{x} (12 x^{2} - 24 x + 24))

derivative of e^{xtan(x})

\frac{d}{d x} (e^{x t a n (x)})

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t an g e n t y = x^{4} + 3 x^{2} - x

fläche y^2=x-1,1,3

a re a y^{2} = x - 1, 1, 3

derivative of (\sqrt[3]{x+1}/(3-4x))

\frac{d}{d x} (\frac{3 x + 1}{3 - 4 x})