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Beliebt Rechnen >

derivative of (x+2(x+6)^3)

Lösung

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

Lösung

(x + 6)^{3} + 3 (x + 6)^{2} (x + 2)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x + 2, g = (x + 6)^{3}

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

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

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

= 1 \cdot (x + 6)^{3} + 3 (x + 6)^{2} (x + 2)

Vereinfache

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(x^4y^5+9x^7y)

\frac{\partial}{\partial x} (x^{4} y^{5} + 9 x^{7} y)

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(x^{2} + 1) y^{^{'}} + y^{2} + 1 = 0

y^'+3/t y=1-2t,y(3)=0

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derivative of sin(2x+y)

\frac{d}{d x} (sin (2 x + y))

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