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Beliebt Rechnen >

derivative of 2x^2cos(2x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

tangent y^2+5x=x^2y-5,(3,5)

t an g e n t y^{2} + 5 x = x^{2} y - 5, (3, 5)

fläche x=y^2,x=3-2y^2

a re a x = y^{2}, x = 3 - 2 y^{2}

integral of (3x)/(sqrt(x^4+6x^2+5))

\int \frac{3 x}{x ^{4} + 6 x ^{2} + 5} d x

derivative of (x^3-1/2)

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

(\partial)/(\partial x)(2xcos(x))

\frac{\partial}{\partial x} (2 x cos (x))