derivative of 3ax^4-4ax^3-5bx^2+7cx

解答

\frac{d}{d x} (3 a x^{4} - 4 a x^{3} - 5 b x^{2} + 7 c x)

12 a x^{3} - 12 a x^{2} - 10 b x + 7 c

求解步骤

\frac{d}{d x} (3 a x^{4} - 4 a x^{3} - 5 b x^{2} + 7 c x)

使用微分加减法定则:

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

= \frac{d}{d x} (3 a x^{4}) - \frac{d}{d x} (4 a x^{3}) - \frac{d}{d x} (5 b x^{2}) + \frac{d}{d x} (7 c x)

\frac{d}{d x} (3 a x^{4}) = 12 a x^{3}

\frac{d}{d x} (4 a x^{3}) = 12 a x^{2}

\frac{d}{d x} (5 b x^{2}) = 10 b x

\frac{d}{d x} (7 c x) = 7 c

= 12 a x^{3} - 12 a x^{2} - 10 b x + 7 c

\int (\frac{1}{x ^{- 3}} + x^{2} e^{3 x^{3}} - \frac{8}{x}) d x

y^{^{'}} + 6 y = e^{- t} - 6

\int e^{4 x} - 5 sin (x) d x

t an g e n t f (x) = \frac{8}{x ^{2} + 4}

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