derivative y=3x^2sin(x)

解

導関数

y = 3 x^{2} sin (x)

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

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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