derivative of xsec(y)

解

\frac{d}{d x} (x sec (y))

sec (y) + x sec (y) tan (y) \frac{d y}{d x}

解答ステップ

\frac{d}{d x} (x sec (y))

積の法則を適用:

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

f = x, g = sec (y)

= \frac{d x}{d x} sec (y) + \frac{d}{d x} (sec (y)) x

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

\frac{d}{d x} (sec (y)) = sec (y) tan (y) \frac{d y}{d x}

= 1 \cdot sec (y) + sec (y) tan (y) \frac{d y}{d x} x

簡素化

= sec (y) + x sec (y) tan (y) \frac{d y}{d x}