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Beliebt Rechnen >

derivative of x^2(x+7^3)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = (x + 7)^{3}

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

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

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

= 2 x (x + 7)^{3} + 3 (x + 7)^{2} x^{2}

Graph

Beliebte Beispiele

x(dy)/(dx)+2y=10x^2

x \frac{d y}{d x} + 2 y = 10 x^{2}

derivative of arctan(3x+2)

\frac{d}{d x} (arctan (3 x + 2))

integral of (2e^{2x})/(e^{2x)+8e^x+15}

\int \frac{2 e ^{2 x}}{e ^{2 x} + 8 e ^{x} + 15} d x

integral of 5arctan(2y)

\int 5 arctan (2 y) d y

integral of x^3ln(3x)

\int x^{3} ln (3 x) d x