derivative of 2xcsc(xsec(x))

解答

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

2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x, g = csc (x) sec (x)

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

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

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

= 2 (1 \cdot csc (x) sec (x) + (- csc^{2} (x) + sec^{2} (x)) x)

化简

2 (1 \cdot csc (x) sec (x) + (- csc^{2} (x) + sec^{2} (x)) x) : 2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))

= 2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))

\frac{d}{d t} (- 4.9 t^{2} + 24.5 t + 6.8)

\int - \frac{1}{64} cos (8 x) d x

n = 0 \sum \infty - 6 \cdot (\frac{6}{7})^{n}

\frac{d}{d x} (x^{4} + 8 x^{3} + 6 x^{2} - 40 x + 25)

x y^{^{'}} + 2 y = - 3 sin (x)