derivative of (x-3x^4tan(x))

解

\frac{d}{d x} ((x - 3 x^{4}) tan (x))

(1 - 12 x^{3}) tan (x) + sec^{2} (x) (x - 3 x^{4})

解答ステップ

\frac{d}{d x} ((x - 3 x^{4}) tan (x))

積の法則を適用:

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

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

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

\frac{d}{d x} (x - 3 x^{4}) = 1 - 12 x^{3}

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

= (1 - 12 x^{3}) tan (x) + sec^{2} (x) (x - 3 x^{4})