derivative of x^4sin(xsin(3x))

解

\frac{d}{d x} (x^{4} \cdot sin (x) \cdot sin (3 x))

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

解答ステップ

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

積の法則を適用:

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

f = x^{4}, g = sin (x) sin (3 x)

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

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

\frac{d}{d x} (sin (x) sin (3 x)) = cos (x) sin (3 x) + cos (3 x) \cdot 3 sin (x)

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