(\partial)/(\partial x)((z)(xsin(xy)-z))

解答

\frac{\partial}{\partial x} ((z) (x sin (x y) - z))

z (x y cos (x y) + sin (x y))

求解步骤

\frac{\partial}{\partial x} ((z) (x sin (x y) - z))

将

z, y

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} (x sin (x y) - z)

使用微分加减法定则:

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

= z (\frac{\partial}{\partial x} (x sin (x y)) - \frac{\partial}{\partial x} (z))

\frac{\partial}{\partial x} (x sin (x y)) = sin (y x) + y x cos (y x)

\frac{\partial}{\partial x} (z) = 0

= z (sin (y x) + y x cos (y x) - 0)

化简

= z (x y cos (x y) + sin (x y))

e x p an d (\frac{2 x ^{4}}{3 x})^{3}

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

e x p an d \frac{x ^{2} ( - 10 x ^{3} + 3 x ^{2} - 60 x )}{20}

\frac{d}{d x} ((z) (x^{2} + y^{2} - 2 z^{2} + 12 x - 8 z - 4))

e x p an d e^{2 (x + 1 - l n ∣ x + 1 ∣)}