derivative of (y^2(csc(x)))

解答

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

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

求解步骤

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

使用微分乘法定则:

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

f = y^{2}, g = csc (x)

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

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

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

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

化简

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

f a c t or α^{2} + α y + αx + x y

f (i) = i^{(25)}

f a c t or \frac{d}{d x} (3 x + 2) + (2 x^{2} + 1)

f a c t or [x^{2} + (3 x + 1)]^{2}

f a c t or d - 1 - 9 d - 9