derivative 2xcsc(x)-x^2cot(x)csc(x)

解答

导数

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

2 csc (x) - 4 x cot (x) csc (x) - x^{2} csc (x) + 2 x^{2} csc^{3} (x)

求解步骤

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

化简

2 (csc (x) - x cot (x) csc (x)) - (2 x cot (x) csc (x) + (csc (x) - 2 csc^{3} (x)) x^{2}) : 2 csc (x) - 4 x cot (x) csc (x) - x^{2} csc (x) + 2 x^{2} csc^{3} (x)

= 2 csc (x) - 4 x cot (x) csc (x) - x^{2} csc (x) + 2 x^{2} csc^{3} (x)

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