(\partial)/(\partial x)(x^4y-4x^3y^2)

解答

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

4 y x^{3} - 12 y^{2} x^{2}

求解步骤

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

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

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

= 4 y x^{3} - 12 y^{2} x^{2}

\int (\frac{3 x}{2} - \frac{9}{4}) e^{x (x - 3)} d x

t an g e n t f (x) = 1 - 2 tan (x), at x = \frac{3 π}{4}

s l o p e y = x^{3} - 15 x

a re a x^{2} = y^{3}, x = 2 y

\int \frac{x ^{2} - 4 x + 7}{x ^{3} - x ^{2} + x + 3} d x