derivative of 4x^3sec(7x)

解

\frac{d}{d x} (4 x^{3} sec (7 x))

4 (3 x^{2} sec (7 x) + sec (7 x) tan (7 x) \cdot 7 x^{3})

解答ステップ

\frac{d}{d x} (4 x^{3} sec (7 x))

定数を除去:

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

= 4 \frac{d}{d x} (x^{3} sec (7 x))

積の法則を適用:

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

f = x^{3}, g = sec (7 x)

= 4 (\frac{d}{d x} (x^{3}) sec (7 x) + \frac{d}{d x} (sec (7 x)) x^{3})

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

\frac{d}{d x} (sec (7 x)) = sec (7 x) tan (7 x) \cdot 7

= 4 (3 x^{2} sec (7 x) + sec (7 x) tan (7 x) \cdot 7 x^{3})