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Beliebt Rechnen >

derivative of 3x^2sin(x)

Lösung

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

Lösung

3 (2 x sin (x) + cos (x) x^{2})

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

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

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

= 3 (2 x sin (x) + cos (x) x^{2})

Graph

Beliebte Beispiele

derivative 1/x sin(x)

d er i v a t i v e \frac{1}{x} sin (x)

derivative of (sin(12x)/(e^{7x)})

\frac{d}{d x} (\frac{sin ( 12 x )}{e ^{7 x}})

integral of 16tan^4(x)sec^6(x)

\int 16 tan^{4} (x) sec^{6} (x) d x

tangent f(x)=38-x^2,(-6,2)

t an g e n t f (x) = 38 - x^{2}, (- 6, 2)

tangent y=3-x^3(0.3)

t an g e n t y = 3 - x^{3} (0.3)