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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Graph

Beliebte Beispiele

derivative of 2^{5x}

\frac{d}{d x} (2^{5 x})

sum from k=1 to infinity of (k^3)/(3^k)

k = 1 \sum \infty \frac{k ^{3}}{3 ^{k}}

y^'+3y=2e^{-3x}

y^{^{'}} + 3 y = 2 e^{- 3 x}

tangent f(x)= 2/x ,\at x=-1

t an g e n t f (x) = \frac{2}{x}, at x = - 1

sum from n=1 to infinity of (2/7)^n

n = 1 \sum \infty (\frac{2}{7})^{n}