de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of 3xsin(x^2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative f(x)=sqrt(2-3x)

d er i v a t i v e f (x) = 2 - 3 x

y^'+5y=0,y(0)=2

y^{^{'}} + 5 y = 0, y (0) = 2

integral of (5x^2-5x+4tan(x))

\int (5 x^{2} - 5 x + 4 tan (x)) d x

integral of (6\sqrt[3]{x})

\int (6 3 x) d x

derivative of 20x(2x^2+7^4)

\frac{d}{d x} (20 x (2 x^{2} + 7)^{4})