derivative of (3x-2^2(5x+4))

解答

\frac{d}{d x} ((3 x - 2)^{2} (5 x + 4))

135 x^{2} - 48 x - 28

求解步骤

\frac{d}{d x} ((3 x - 2)^{2} (5 x + 4))

使用微分乘法定则:

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

f = (3 x - 2)^{2}, g = 5 x + 4

= \frac{d}{d x} ((3 x - 2)^{2}) (5 x + 4) + \frac{d}{d x} (5 x + 4) (3 x - 2)^{2}

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

\frac{d}{d x} (5 x + 4) = 5

= 6 (3 x - 2) (5 x + 4) + 5 (3 x - 2)^{2}

化简

6 (3 x - 2) (5 x + 4) + 5 (3 x - 2)^{2} : 135 x^{2} - 48 x - 28

= 135 x^{2} - 48 x - 28

\int (8 x + 3) (7 - x) d x

x \to - \infty lim (- 3 x + x)

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\int \frac{x x}{2} d x

d er i v a t i v e f (x) = \frac{( 4 x + x ^{2} )}{( 2 + x ) ^{2}}