(\partial)/(\partial x)(y^8+4x^3y^3)

解答

\frac{\partial}{\partial x} (y^{8} + 4 x^{3} y^{3})

12 y^{3} x^{2}

求解步骤

\frac{\partial}{\partial x} (y^{8} + 4 x^{3} y^{3})

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} (y^{8}) + \frac{\partial}{\partial x} (4 x^{3} y^{3})

\frac{\partial}{\partial x} (y^{8}) = 0

\frac{\partial}{\partial x} (4 x^{3} y^{3}) = 12 y^{3} x^{2}

= 0 + 12 y^{3} x^{2}

化简

= 12 y^{3} x^{2}

d er i v a t i v e [x^{2} (x^{2} + 6 x)]^{6}

\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 3 x} d x

d er i v a t i v e 4 v^{2} - 2

x \to 0 lim (\frac{1}{x} sin (\frac{1}{x}))

\int 18 cos^{2} (x) sin (x) d x