(\partial}{\partial x}(\frac{x^2+y^2)/2)

解答

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

x

求解步骤

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

将

y

视为常数

将常数提出:

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

= \frac{1}{2} \frac{\partial}{\partial x} (x^{2} + y^{2})

使用微分加减法定则:

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

= \frac{1}{2} (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (y^{2}))

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

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

= \frac{1}{2} (2 x + 0)

化简

\frac{1}{2} (2 x + 0) : x

= x

y^{^{''}} - \frac{2}{x} y^{^{'}} - \frac{10}{x ^{2}} y = 0

d er i v a t i v e cos (4 x)

t an g e n t 3 x + 4, at x = 4

\frac{d}{d x} (\frac{5 x}{( x ^{2} + 2 ) ^{2}})

f (x) = e^{x} x + 2 e^{x}