derivative 4v^4-(12v^3+9v)

解答

导数

4 v^{4} - (12 v^{3} + 9 v)

16 v^{3} - 36 v^{2} - 9

求解步骤

\frac{d}{d v} (4 v^{4} - (12 v^{3} + 9 v))

化简

4 v^{4} - (12 v^{3} + 9 v) : 4 v^{4} - 12 v^{3} - 9 v

= \frac{d}{d v} (4 v^{4} - 12 v^{3} - 9 v)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d v} (4 v^{4}) - \frac{d}{d v} (12 v^{3}) - \frac{d}{d v} (9 v)

\frac{d}{d v} (4 v^{4}) = 16 v^{3}

\frac{d}{d v} (12 v^{3}) = 36 v^{2}

\frac{d}{d v} (9 v) = 9

= 16 v^{3} - 36 v^{2} - 9

\frac{d y}{d x} = \frac{( x - y )}{x + y}

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

\int \frac{x ^{4} + 3 x ^{2} + 5}{x ^{4}} d x

\frac{d x}{d t} = 8 + 4 sin (\frac{t}{4}) - \frac{x}{100}, x (0) = 70

t an g e n t f (x) = \frac{x}{2 x - 8}, at x = 3