derivative (x-1)^2(2x+1)^4

Lösung

ableitung von

(x - 1)^{2} (2 x + 1)^{4}

2 (x - 1) (2 x + 1)^{4} + 8 (2 x + 1)^{3} (x - 1)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = (x - 1)^{2}, g = (2 x + 1)^{4}

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

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

\frac{d}{d x} ((2 x + 1)^{4}) = 8 (2 x + 1)^{3}

= 2 (x - 1) (2 x + 1)^{4} + 8 (2 x + 1)^{3} (x - 1)^{2}

\frac{\partial}{\partial x} (e^{x^{2} - y^{2}})

y^{^{'}} + 2 x^{2} y = x^{2}

\int \frac{2 - 2 x}{1 - x} d x

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\frac{\partial}{\partial x} (arctan (9 x))