(\partial)/(\partial y)((4sqrt(x))/(3y^2+1))

解答

\frac{\partial}{\partial y} (\frac{4 x}{3 y ^{2} + 1})

- \frac{24 y x}{( 3 y ^{2} + 1 ) ^{2}}

求解步骤

\frac{\partial}{\partial y} (\frac{4 x}{3 y ^{2} + 1})

将

x

视为常数

将常数提出:

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

= 4 x \frac{\partial}{\partial y} (\frac{1}{3 y ^{2} + 1})

使用指数法则:

\frac{1}{a} = a^{- 1}

= 4 x \frac{\partial}{\partial y} ((3 y^{2} + 1)^{- 1})

使用连锁律:

- \frac{1}{( 3 y ^{2} + 1 ) ^{2}} \frac{\partial}{\partial y} (3 y^{2} + 1)

= - \frac{1}{( 3 y ^{2} + 1 ) ^{2}} \frac{\partial}{\partial y} (3 y^{2} + 1)

\frac{\partial}{\partial y} (3 y^{2} + 1) = 6 y

= 4 x (- \frac{1}{( 3 y ^{2} + 1 ) ^{2}} \cdot 6 y)

化简

4 x (- \frac{1}{( 3 y ^{2} + 1 ) ^{2}} \cdot 6 y) : - \frac{24 y x}{( 3 y ^{2} + 1 ) ^{2}}

= - \frac{24 y x}{( 3 y ^{2} + 1 ) ^{2}}

x \to 2 lim (3 + x)

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2}})

a re a sin (x), 5 x, \frac{π}{2}, π

x \to - 2 lim (x + 3)

d er i v a t i v e f (x) = (x^{2} - 5) e^{x}