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Beliebt Rechnen >

derivative 9x(2x^2+1)

Lösung

ableitung von

9 x (2 x^{2} + 1)

Lösung

9 (6 x^{2} + 1)

Schritte zur Lösung

\frac{d}{d x} (9 x (2 x^{2} + 1))

Entferne die Konstante:

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

= 9 \frac{d}{d x} (x (2 x^{2} + 1))

Wende die Produktregel an:

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

f = x, g = 2 x^{2} + 1

= 9 (\frac{d x}{d x} (2 x^{2} + 1) + \frac{d}{d x} (2 x^{2} + 1) x)

\frac{d x}{d x} = 1

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

= 9 (1 \cdot (2 x^{2} + 1) + 4 xx)

Vereinfache

9 (1 \cdot (2 x^{2} + 1) + 4 xx) : 9 (6 x^{2} + 1)

= 9 (6 x^{2} + 1)

Graph

Beliebte Beispiele

steigung 2sqrt(x)

s l o p e 2 x

integral of sqrt(9t^2+4)

\int 9 t^{2} + 4 d t

(\partial)/(\partial x)(9/(x^2+y^2))

\frac{\partial}{\partial x} (\frac{9}{x ^{2} + y ^{2}})

integral of (5x^4-6x^2+3)

\int (5 x^{4} - 6 x^{2} + 3) d x

derivative of ln(e^x+3)

\frac{d}{d x} (ln (e^{x} + 3))