(\partial)/(\partial x)(2+yln(4+x(y)^2))

解答

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

\frac{y ^{3}}{y ^{2} x + 4}

求解步骤

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

将

y

视为常数

使用微分加减法定则:

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

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

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

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

= 0 + \frac{y ^{3}}{4 + y ^{2} x}

化简

= \frac{y ^{3}}{y ^{2} x + 4}

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

d er i v a t i v e f (x) = 3^{s i n (3 x)}

\int \frac{2 + w ^{4}}{w ^{3} + 9 w} d w

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

d er i v a t i v e sin^{3} (4 x)