derivative of x^3cot(x)

解

\frac{d}{d x} (x^{3} cot (x))

3 x^{2} cot (x) - x^{3} csc^{2} (x)

解答ステップ

\frac{d}{d x} (x^{3} cot (x))

積の法則を適用:

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

f = x^{3}, g = cot (x)

= \frac{d}{d x} (x^{3}) cot (x) + \frac{d}{d x} (cot (x)) x^{3}

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

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

= 3 x^{2} cot (x) + (- csc^{2} (x)) x^{3}

簡素化

= 3 x^{2} cot (x) - x^{3} csc^{2} (x)