derivative of sin({p}(x)ix)

解

\frac{d}{d x} (sin (p (x)) i x)

i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))

解答ステップ

\frac{d}{d x} (sin (p (x)) i x)

定数を除去:

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

= i \frac{d}{d x} (sin (p (x)) x)

積の法則を適用:

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

f = sin (p (x)), g = x

= i (\frac{d}{d x} (sin (p (x))) x + \frac{d x}{d x} sin (p (x)))

\frac{d}{d x} (sin (p (x))) = cos (p (x)) \frac{d}{d x} (p (x))

\frac{d x}{d x} = 1

= i (cos (p (x)) \frac{d}{d x} (p (x)) x + 1 \cdot sin (p (x)))

簡素化

i (cos (p (x)) \frac{d}{d x} (p (x)) x + 1 \cdot sin (p (x))) : i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))

= i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))