derivative of x^3(3x-8)

解答

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

12 x^{3} - 24 x^{2}

求解步骤

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

使用微分乘法定则:

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

f = x^{3}, g = 3 x - 8

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

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

\frac{d}{d x} (3 x - 8) = 3

= 3 x^{2} (3 x - 8) + 3 x^{3}

化简

3 x^{2} (3 x - 8) + 3 x^{3} : 12 x^{3} - 24 x^{2}

= 12 x^{3} - 24 x^{2}

\int_{6}^{11} 10 arccot (x) d x

d er i v a t i v e f (x) = sin (sin (8 e^{x}))

\int \frac{1}{u ^{2} - a ^{2}} d u

d er i v a t i v e x^{8} (x - 4)^{7}

\frac{d}{d x} (cos (2^{3 x^{2} + 5 x - 6}))