derivative of (2x/(sin(x)))

解答

\frac{d}{d x} (\frac{2 x}{sin ( x )})

2 (csc (x) - x cot (x) csc (x))

求解步骤

\frac{d}{d x} (\frac{2 x}{sin ( x )})

化简

\frac{2 x}{sin ( x )} : 2 x csc (x)

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x, g = csc (x)

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

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

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

= 2 (1 \cdot csc (x) + (- cot (x) csc (x)) x)

化简

= 2 (csc (x) - x cot (x) csc (x))

d er i v a t i v e \frac{b ( - 12 b - 290 )}{8 - b}

\int cos (\frac{nπ x}{3}) d x

(x^{2} + 1) d x + \frac{d y}{y} = 0, y (- 1) = 1

d er i v a t i v e \frac{( 3 + 2 x )}{( 1 + x )}

\int cos^{2} (θ) sin (θ) d θ