derivative 3(x^2+5x)^3

解答

导数

3 (x^{2} + 5 x)^{3}

9 (x^{2} + 5 x)^{2} (2 x + 5)

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用连锁律:

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

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

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

= 3 \cdot 3 (x^{2} + 5 x)^{2} (2 x + 5)

化简

= 9 (x^{2} + 5 x)^{2} (2 x + 5)

\frac{d}{d x} (6 x \cdot sin (3 x^{2}))

\frac{d}{d x} (ln (\frac{4 - x}{4 + x}))

\int_{0}^{3} c (3 - x) d x

\int \frac{5 x - 3}{x + 1} d x

d er i v a t i v e f (x) = \frac{4}{3 x ^{2}}