derivative of-2cot(x+6x^4csc(x))

解答

\frac{d}{d x} (- 2 cot (x) + 6 x^{4} csc (x))

2 csc^{2} (x) + 6 (4 x^{3} csc (x) - x^{4} cot (x) csc (x))

求解步骤

\frac{d}{d x} (- 2 cot (x) + 6 x^{4} csc (x))

使用微分加减法定则:

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

= - \frac{d}{d x} (2 cot (x)) + \frac{d}{d x} (6 x^{4} csc (x))

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

\frac{d}{d x} (6 x^{4} csc (x)) = 6 (4 x^{3} csc (x) - x^{4} cot (x) csc (x))

= - (- 2 csc^{2} (x)) + 6 (4 x^{3} csc (x) - x^{4} cot (x) csc (x))

化简

= 2 csc^{2} (x) + 6 (4 x^{3} csc (x) - x^{4} cot (x) csc (x))

d er i v a t i v e f (x) = x^{\frac{1}{9}}

\frac{d}{d x} (8 - 5 x)

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

\int (2 x^{3} + x) (x^{4} + x^{2})^{108} d x

f (x) = sin (9 x)