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Beliebt Rechnen >

derivative of sin(3x^2cos(2x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= sin (3) \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)

= sin (3) (\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

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

Vereinfache

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

Graph

Beliebte Beispiele

integral of t*e^t

\int t \cdot e^{t} d t

y^{''}-y^'+121y=11sin(11t)

y^{^{''}} - y^{^{'}} + 121 y = 11 sin (11 t)

integral of 1/(xsqrt(x-2))

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

y^{''}+4y^'+4y=e^{2x}

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{2 x}

integral of 1/(x+1)

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