derivative 3xe^xcsc(x)

解答

导数

3 x e^{x} csc (x)

3 (e^{x} csc (x) + x (e^{x} csc (x) - e^{x} cot (x) csc (x)))

求解步骤

\frac{d}{d x} (3 x e^{x} csc (x))

将常数提出:

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

= 3 \frac{d}{d x} (x e^{x} csc (x))

使用微分乘法定则:

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

f = x, g = e^{x} csc (x)

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

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

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

= 3 (1 \cdot e^{x} csc (x) + (e^{x} csc (x) - e^{x} cot (x) csc (x)) x)

化简

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

x \to 0 lim (sin^{2} (x) (\frac{1}{x}))

x \to - 1 lim (\frac{1}{x ^{2} + 1})

n = 0 \sum \infty \frac{6}{5 ^{n}}

\int 2 sec (2 x) tan (2 x) d x

y^{^{'}} + (\frac{1}{x}) y = 8 x^{2}