derivative of x^2-xy+y^2

解答

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

2 x - y - x \frac{d y}{d x} + 2 y \frac{d y}{d x}

求解步骤

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

使用微分加减法定则:

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

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

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

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

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

= 2 x - (y + x \frac{d y}{d x}) + 2 y \frac{d y}{d x}

化简

= 2 x - y - x \frac{d y}{d x} + 2 y \frac{d y}{d x}

\int_{0}^{1} \frac{63}{4 y - 1} d y

d er i v a t i v e e^{x} (3 x^{2} - 6 x + 6)

x \to 0 - lim (7 - 2 x)

\int 3 x^{3} - 5 x^{2} + 3 x + 4 d x

d er i v a t i v e (x + 1)^{x + 1}