derivative of 2xcsc(xsec(x))

解

\frac{d}{d x} (2 x csc (x) sec (x))

2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))

解答ステップ

\frac{d}{d x} (2 x csc (x) sec (x))

定数を除去:

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

= 2 \frac{d}{d x} (x csc (x) sec (x))

積の法則を適用:

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

f = x, g = csc (x) sec (x)

= 2 (\frac{d x}{d x} csc (x) sec (x) + \frac{d}{d x} (csc (x) sec (x)) x)

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

\frac{d}{d x} (csc (x) sec (x)) = - csc^{2} (x) + sec^{2} (x)

= 2 (1 \cdot csc (x) sec (x) + (- csc^{2} (x) + sec^{2} (x)) x)

簡素化

2 (1 \cdot csc (x) sec (x) + (- csc^{2} (x) + sec^{2} (x)) x) : 2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))

= 2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))