d/(dy)((x)(y+(x^2y)h-2x*h-n))

解答

\frac{d}{d y} ((x) (y + (x^{2} \cdot y) \cdot h - 2 x \cdot h - n))

x (x^{2} h + 1)

求解步骤

\frac{d}{d y} ((x) (y + (x^{2} y) h - 2 x h - n))

将

n, x, h

视为常数

将常数提出:

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

= x \frac{d}{d y} (y + x^{2} y h - 2 x h - n)

使用微分加减法定则:

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

= x (\frac{d y}{d y} + \frac{d}{d y} (x^{2} y h) - \frac{d}{d y} (2 x h) - \frac{d n}{d y})

\frac{d y}{d y} = 1

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

\frac{d}{d y} (2 x h) = 0

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

= x (1 + x^{2} h - 0 - 0)

化简

= x (x^{2} h + 1)

e x p an d \frac{1}{3} (6)^{3} - 5 (6)^{2} + 24 (6)

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

s im pl i f y 12 (6 x y + 7) (y + x (\frac{d}{d x} ((y) y)))

s im pl i f y 8 (\frac{w}{4} + \frac{3}{2})

e x p an d \frac{1}{s + 1} + 2 s + 2 + (\frac{1}{s + 1})