derivative f(x)=(x^2+4x+3)^2

解答

导数

f (x) = (x^{2} + 4 x + 3)^{2}

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

求解步骤

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

使用连锁律:

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

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

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

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