derivative of-xy^3

解答

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

- y^{3} - 3 x y^{2} \frac{d y}{d x}

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = y^{3}

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

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

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

= - (1 \cdot y^{3} + 3 y^{2} \frac{d y}{d x} x)

化简

- (1 \cdot y^{3} + 3 y^{2} \frac{d y}{d x} x) : - y^{3} - 3 x y^{2} \frac{d y}{d x}

= - y^{3} - 3 x y^{2} \frac{d y}{d x}

s l o p e (- 2, 4), (- 1, - 1)

\int_{- a}^{a} (a - ∣ x ∣) d x

a \to 0 lim (x^{a})

t an g e n t \frac{x + 7}{x + 1}

t an g e n t y = 4 x^{3} - 4 x, (1, 0)