derivative f(x)=x^4sin(2x)

解

導関数

f (x) = x^{4} sin (2 x)

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

解答ステップ

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

積の法則を適用:

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

f = x^{4}, g = sin (2 x)

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

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