derivative of (4x^3-6(4x^2+4))

解答

\frac{d}{d x} ((4 x^{3} - 6) (4 x^{2} + 4))

80 x^{4} + 48 x^{2} - 48 x

求解步骤

\frac{d}{d x} ((4 x^{3} - 6) (4 x^{2} + 4))

使用微分乘法定则:

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

f = 4 x^{3} - 6, g = 4 x^{2} + 4

= \frac{d}{d x} (4 x^{3} - 6) (4 x^{2} + 4) + \frac{d}{d x} (4 x^{2} + 4) (4 x^{3} - 6)

\frac{d}{d x} (4 x^{3} - 6) = 12 x^{2}

\frac{d}{d x} (4 x^{2} + 4) = 8 x

= 12 x^{2} (4 x^{2} + 4) + 8 x (4 x^{3} - 6)

化简

12 x^{2} (4 x^{2} + 4) + 8 x (4 x^{3} - 6) : 80 x^{4} + 48 x^{2} - 48 x

= 80 x^{4} + 48 x^{2} - 48 x

\int \frac{1}{( 1 - x ^{2} ) ^{3}} d x

\frac{d}{d x} (\frac{ln ( x )}{9 x})

\int (\frac{1}{e ^{3 t}}) d t

x \to 0 lim (\frac{e - 1}{x})

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