derivative y=x^3(2x+3)^7

解答

导数

y = x^{3} (2 x + 3)^{7}

3 x^{2} (2 x + 3)^{7} + 14 (2 x + 3)^{6} x^{3}

求解步骤

\frac{d}{d x} (x^{3} (2 x + 3)^{7})

使用微分乘法定则:

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

f = x^{3}, g = (2 x + 3)^{7}

= \frac{d}{d x} (x^{3}) (2 x + 3)^{7} + \frac{d}{d x} ((2 x + 3)^{7}) x^{3}

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

\frac{d}{d x} ((2 x + 3)^{7}) = 14 (2 x + 3)^{6}

= 3 x^{2} (2 x + 3)^{7} + 14 (2 x + 3)^{6} x^{3}

a re a 3 x, \frac{3}{x}, x = 3

\frac{d y}{d x} = - \frac{y}{x}

x \to 0 lim (cos (π))

a re a x + y = 10, (2, 8)

\int \frac{2 x ^{3} + x - 1}{x ^{3} + x ^{2} - 4 x - 4} d x