derivative of x^3-12xy+8y^3

解答

\frac{d}{d x} (x^{3} - 12 x y + 8 y^{3})

3 x^{2} - 12 (y + x \frac{d y}{d x}) + 24 y^{2} \frac{d y}{d x}

求解步骤

\frac{d}{d x} (x^{3} - 12 x y + 8 y^{3})

使用微分加减法定则:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (12 x y) + \frac{d}{d x} (8 y^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (12 x y) = 12 (y + x \frac{d y}{d x})

\frac{d}{d x} (8 y^{3}) = 24 y^{2} \frac{d y}{d x}

= 3 x^{2} - 12 (y + x \frac{d y}{d x}) + 24 y^{2} \frac{d y}{d x}

\int (x - 1) (x + 2) d x

d er i v a t i v e f (x) = 5 x^{\frac{4}{5}} - 2 x^{\frac{2}{7}}

d er i v a t i v e \frac{1}{x + 5}

\int t (2 t - 3 t) d t

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