derivative of 4e^{3x^2}sin(cos(2x))

解

\frac{d}{d x} (4 e^{3 x^{2}} sin (cos (2 x)))

4 (6 e^{3 x^{2}} x sin (cos (2 x)) - 2 e^{3 x^{2}} cos (cos (2 x)) sin (2 x))

解答ステップ

\frac{d}{d x} (4 e^{3 x^{2}} sin (cos (2 x)))

定数を除去:

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

= 4 \frac{d}{d x} (e^{3 x^{2}} sin (cos (2 x)))

積の法則を適用:

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

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

= 4 (\frac{d}{d x} (e^{3 x^{2}}) sin (cos (2 x)) + \frac{d}{d x} (sin (cos (2 x))) e^{3 x^{2}})

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

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

= 4 (e^{3 x^{2}} \cdot 6 x sin (cos (2 x)) + (- 2 cos (cos (2 x)) sin (2 x)) e^{3 x^{2}})

簡素化

= 4 (6 e^{3 x^{2}} x sin (cos (2 x)) - 2 e^{3 x^{2}} cos (cos (2 x)) sin (2 x))