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Beliebt Rechnen >

derivative of x^2(x+3^4)

Lösung

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

Lösung

2 x (x + 3)^{4} + 4 (x + 3)^{3} x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = (x + 3)^{4}

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

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

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

= 2 x (x + 3)^{4} + 4 (x + 3)^{3} x^{2}

Graph

Beliebte Beispiele

sum from n=1 to infinity of (5^n)/(6^nn)

n = 1 \sum \infty \frac{5 ^{n}}{6 ^{n} n}

x y^{^{'}} + y = 3 x y

integral of (x^2+7x-3)sin(2x)

\int (x^{2} + 7 x - 3) sin (2 x) d x

integral of 3/(x(x^2+1))

\int \frac{3}{x ( x ^{2} + 1 )} d x

derivative of |(-3^x|)

\frac{d}{d x} (∣ (- 3)^{x} ∣)