derivative of 6x*sin(3x^2)

Lösung

\frac{d}{d x} (6 x \cdot sin (3 x^{2}))

6 (sin (3 x^{2}) + 6 x^{2} cos (3 x^{2}))

Schritte zur Lösung

\frac{d}{d x} (6 x sin (3 x^{2}))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x sin (3 x^{2}))

Wende die Produktregel an:

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

f = x, g = sin (3 x^{2})

= 6 (\frac{d x}{d x} sin (3 x^{2}) + \frac{d}{d x} (sin (3 x^{2})) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (3 x^{2})) = cos (3 x^{2}) \cdot 6 x

= 6 (1 \cdot sin (3 x^{2}) + cos (3 x^{2}) \cdot 6 xx)

Vereinfache

6 (1 \cdot sin (3 x^{2}) + cos (3 x^{2}) \cdot 6 xx) : 6 (sin (3 x^{2}) + 6 x^{2} cos (3 x^{2}))

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

\frac{d}{d x} (ln (\frac{4 - x}{4 + x}))

\int_{0}^{3} c (3 - x) d x

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