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Beliebt Rechnen >

derivative of x^4sin(3x)

Lösung

\frac{d}{d x} (x^{4} sin (3 x))

Lösung

4 x^{3} sin (3 x) + cos (3 x) \cdot 3 x^{4}

Schritte zur Lösung

\frac{d}{d x} (x^{4} sin (3 x))

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= 4 x^{3} sin (3 x) + cos (3 x) \cdot 3 x^{4}

Graph

Beliebte Beispiele

derivative y=xsin(3/x)

d er i v a t i v e y = x sin (\frac{3}{x})

integral of (x^7)/(sqrt(x^4-3))

\int \frac{x ^{7}}{x ^{4} - 3} d x

steigung (-7,-4),(8,8)

s l o p e (- 7, - 4), (8, 8)

sum from n=1 to infinity of (6^n)/((4+11^n))

n = 1 \sum \infty \frac{6 ^{n}}{( 4 + 1 1 ^{n} )}

integral of 4/(x^2+25)

\int \frac{4}{x ^{2} + 25} d x