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Beliebt Rechnen >

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

Lösung

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

Lösung

18 x^{2} - 18 x + 8

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (3 x^{2} + 4) = 6 x

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

= 6 x (2 x - 3) + 2 (3 x^{2} + 4)

Vereinfache

6 x (2 x - 3) + 2 (3 x^{2} + 4) : 18 x^{2} - 18 x + 8

= 18 x^{2} - 18 x + 8

Graph

Beliebte Beispiele

integral of 5/x+e^x

\int \frac{5}{x} + e^{x} d x

tangent y=5+5x^2-2x^3

t an g e n t y = 5 + 5 x^{2} - 2 x^{3}

integral of (x-5)^2e^x

\int (x - 5)^{2} e^{x} d x

limit as x approaches 8+of 1/((x-8)^2)

x \to 8 + lim (\frac{1}{( x - 8 ) ^{2}})

y^{^{'}} + 3 y = 3