derivative of 7x^2cos(xcot(x))

解

\frac{d}{d x} (7 x^{2} cos (x) cot (x))

7 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

解答ステップ

\frac{d}{d x} (7 x^{2} cos (x) cot (x))

定数を除去:

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

= 7 \frac{d}{d x} (x^{2} cos (x) cot (x))

積の法則を適用:

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

f = x^{2}, g = cos (x) cot (x)

= 7 (\frac{d}{d x} (x^{2}) cos (x) cot (x) + \frac{d}{d x} (cos (x) cot (x)) x^{2})

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

\frac{d}{d x} (cos (x) cot (x)) = - cos (x) - cot (x) csc (x)

= 7 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})