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Beliebt Rechnen >

derivative of 2(sin(x^2+2x^2cos(x^2)))

Lösung

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

Lösung

2 (6 x cos (x^{2}) - 4 x^{3} sin (x^{2}))

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Multipliziere aus

cos (x^{2}) \cdot 2 x + 2 (2 x cos (x^{2}) - 2 x^{3} sin (x^{2})) : 6 x cos (x^{2}) - 4 x^{3} sin (x^{2})

= 2 (6 x cos (x^{2}) - 4 x^{3} sin (x^{2}))

Graph

Beliebte Beispiele

integral of (6x)/(\sqrt[5]{(x^2+7)^2)}

\int \frac{6 x}{5 ( x ^{2} + 7 ) ^{2}} d x

derivative of (x^{10}-1^3)

\frac{d}{d x} ((x^{10} - 1)^{3})

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

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

integral of xos(8x^2+pi)

\int x os (8 x^{2} + π) d x

derivative of (x^2+4x+6^5)

\frac{d}{d x} ((x^{2} + 4 x + 6)^{5})