derivative (x-4)^3+3x(x-4)^2

解答

导数

(x - 4)^{3} + 3 x (x - 4)^{2}

12 x^{2} - 72 x + 96

求解步骤

\frac{d}{d x} ((x - 4)^{3} + 3 x (x - 4)^{2})

化简

(x - 4)^{3} + 3 x (x - 4)^{2} : 4 x^{3} - 36 x^{2} + 96 x - 64

= \frac{d}{d x} (4 x^{3} - 36 x^{2} + 96 x - 64)

使用微分加减法定则:

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

= \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (36 x^{2}) + \frac{d}{d x} (96 x) - \frac{d}{d x} (64)

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

\frac{d}{d x} (36 x^{2}) = 72 x

\frac{d}{d x} (96 x) = 96

\frac{d}{d x} (64) = 0

= 12 x^{2} - 72 x + 96 - 0

化简

= 12 x^{2} - 72 x + 96

x \to - \infty lim (x^{6})

\frac{\partial}{\partial x} (- 4 cos (3 x))

\int \frac{12 s + 12}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

\int \frac{1}{4 - x ^{2}} d x

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