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Beliebt Rechnen >

(\partial)/(\partial x)(x^2sin(x))

Lösung

\frac{\partial}{\partial x} (x^{2} sin (x))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial 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{\partial}{\partial x} (x^{2}) sin (x) + \frac{\partial}{\partial x} (sin (x)) x^{2}

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

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

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

Beliebte Beispiele

integral of 1/(2xsqrt(x))

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

integral of ln(x)sqrt(x^{13)}

\int ln (x) x^{13} d x

derivative of 1/(4x+4)

\frac{d}{d x} (\frac{1}{4 x + 4})

f (y) = e^{y}

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

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