d/(dy)((x)(xy+sin(xy)+x))

解答

\frac{d}{d y} ((x) (x y + sin (x y) + x))

x (x + x cos (x y))

求解步骤

\frac{d}{d y} ((x) (x y + sin (x y) + x))

将

x

视为常数

将常数提出:

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

= x \frac{d}{d y} (x y + sin (x y) + x)

使用微分加减法定则:

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

= x (\frac{d}{d y} (x y) + \frac{d}{d y} (sin (x y)) + \frac{d x}{d y})

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

\frac{d}{d y} (sin (x y)) = cos (x y) x

\frac{d x}{d y} = 0

= x (x + cos (x y) x + 0)

化简

= x (x + x cos (x y))

e x p an d \frac{( 4 x - 3 ) ( x + 2 )}{8 x + 6}

e x p an d 1 (- 4 x + 2 y = 6)

e x p an d \frac{( 2 x - 1 )}{( 3 x - 1 ) ( x - 1 )}

e x p an d \frac{5 ( 3 30 - 10 )}{34}

e x p an d \frac{689}{96 ( 2 x - 1 )}