de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of x^3sin(x^2)

Lösung

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

Lösung

3 x^{2} sin (x^{2}) + 2 x^{4} cos (x^{2})

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

cos (x^{2}) \cdot 2 x x^{3} = 2 x^{4} cos (x^{2})

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

Graph

Beliebte Beispiele

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

derivative-2x^4

d er i v a t i v e - 2 x^{4}

derivative y= 6/x

d er i v a t i v e y = \frac{6}{x}

integral of ((3x+1)^{1/2})/2

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

integral of sin^6(4x)

\int sin^{6} (4 x) d x