(\partial)/(\partial x)((z)(z^2-5x^2+y^2))

解答

\frac{\partial}{\partial x} ((z) (z^{2} - 5 x^{2} + y^{2}))

- 10 z x

求解步骤

\frac{\partial}{\partial x} ((z) (z^{2} - 5 x^{2} + y^{2}))

将

z, y

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} (z^{2} - 5 x^{2} + y^{2})

使用微分加减法定则:

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

= z (\frac{\partial}{\partial x} (z^{2}) - \frac{\partial}{\partial x} (5 x^{2}) + \frac{\partial}{\partial x} (y^{2}))

\frac{\partial}{\partial x} (z^{2}) = 0

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

\frac{\partial}{\partial x} (y^{2}) = 0

= z (0 - 10 x + 0)

化简

= - 10 z x

e x p an d (4 x^{3} e^{x}) (x^{2} + 1)

s im pl i f y (x + \frac{1}{2}) (x - 1) (x - \frac{3}{4})

s im pl i f y 2 (sin (t)) (t) (7 - t^{2})

e x p an d (2 t^{3} + 3 y) d t

s im pl i f y (- x - 2 + 1)^{2}