derivative of e^xcot(y+2ycsc(y))

解答

\frac{d}{d x} (e^{x} cot (y) + 2 y csc (y))

e^{x} cot (y) - e^{x} csc^{2} (y) \frac{d y}{d x} + 2 (csc (y) \frac{d y}{d x} - cot (y) csc (y) \frac{d y}{d x} y)

求解步骤

\frac{d}{d x} (e^{x} cot (y) + 2 y csc (y))

使用微分加减法定则:

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

= \frac{d}{d x} (e^{x} cot (y)) + \frac{d}{d x} (2 y csc (y))

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

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

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

\int \frac{1}{2 ( x - 2 )} d x

\int_{0}^{1} x^{2} e^{x^{3} - 1} d x

\frac{\partial}{\partial x} (x^{2} + y^{3} + w^{4})

a re a y = ∣ 3 x ∣, y = x^{2} - 4

\int \frac{1}{1 - 4 x} d x