derivative of ((x^2+1^2)/(2x))

解答

\frac{d}{d x} (\frac{( x ^{2} + 1 ) ^{2}}{2 x})

\frac{3 x ^{4} + 2 x ^{2} - 1}{2 x ^{2}}

求解步骤

\frac{d}{d x} (\frac{( x ^{2} + 1 ) ^{2}}{2 x})

将常数提出:

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

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

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( ( x ^{2} + 1 ) ^{2} ) x - \frac{d x}{d x} ( x ^{2} + 1 ) ^{2}}{x ^{2}}

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

\frac{d x}{d x} = 1

= \frac{1}{2} \cdot \frac{4 x ( x ^{2} + 1 ) x - 1 \cdot ( x ^{2} + 1 ) ^{2}}{x ^{2}}

化简

\frac{1}{2} \cdot \frac{4 x ( x ^{2} + 1 ) x - 1 \cdot ( x ^{2} + 1 ) ^{2}}{x ^{2}} : \frac{3 x ^{4} + 2 x ^{2} - 1}{2 x ^{2}}

= \frac{3 x ^{4} + 2 x ^{2} - 1}{2 x ^{2}}

t an g e n t y = cos (x), at x = - \frac{π}{2}

x \to 0 lim (e^{x} - 2 x^{2})

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

\frac{d}{d x} (lo g_{3} (5 x + 2))

y^{2} \cdot (\frac{d y}{d x}) + y^{3} = 1