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Beliebt Rechnen >

derivative f(x)=x^2*sin(x)

Lösung

ableitung von

f (x) = x^{2} \cdot sin (x)

Lösung

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

Schritte zur Lösung

\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)

= \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)

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

Graph

Beliebte Beispiele

derivative of ((x^3-1)/((x^3+1)))

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

tangent y=0.03x^2+1

t an g e n t y = 0.03 x^{2} + 1

integral from 2 to 3 of 1/(4-3x)

\int_{2}^{3} \frac{1}{4 - 3 x} d x

integral of-3cos(x)

\int - 3 cos (x) d x

derivative of x^7(x-12^5)

\frac{d}{d x} (x^{7} (x - 12)^{5})