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Beliebt Rechnen >

derivative of \sqrt[3]{x^2}sin(5x)

Lösung

\frac{d}{d x} (3 x^{2} sin (5 x))

Lösung

\frac{2 sin ( 5 x )}{3 x ^{\frac{1}{3}}} + 5 cos (5 x) 3 x^{2}

Schritte zur Lösung

\frac{d}{d x} (3 x^{2} sin (5 x))

Wende die Produktregel an:

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

f = 3 x^{2}, g = sin (5 x)

= \frac{d}{d x} (3 x^{2}) sin (5 x) + \frac{d}{d x} (sin (5 x)) 3 x^{2}

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= \frac{2}{3 x ^{\frac{1}{3}}} sin (5 x) + cos (5 x) \cdot 5 3 x^{2}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 sin ( 5 x )}{3 x ^{\frac{1}{3}}} + 5 cos (5 x) 3 x^{2}

Graph

Beliebte Beispiele

derivative of arctanh(x)

\frac{d}{d x} (arctanh (x))

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\int 5 x ln (5 x) d x

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

fläche y=(7t-4),(0,0.5)

a re a y = (7 t - 4), (0, 0.5)

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\frac{d}{d x} (x^{t a n (x)})