derivative xe^xcsc(x)

解答

导数

x e^{x} csc (x)

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

求解步骤

\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)

= \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)

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

化简

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

\int 6 y^{2} + \frac{1}{24 y ^{2}} d y

d er i v a t i v e - 5 π sin (10 π x)

\frac{\partial}{\partial y} (4 x^{3} y)

x \to 0 + lim (\frac{7 e ^{x}}{x ^{5}})

x \to 0 lim (\frac{e ^{0} - 1}{x})