derivative f(t)=(t^2+3t+7)(3t^2+3)

解答

导数

f (t) = (t^{2} + 3 t + 7) (3 t^{2} + 3)

12 t^{3} + 27 t^{2} + 48 t + 9

求解步骤

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

使用微分乘法定则:

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

f = t^{2} + 3 t + 7, g = 3 t^{2} + 3

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

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

\frac{d}{d t} (3 t^{2} + 3) = 6 t

= (2 t + 3) (3 t^{2} + 3) + 6 t (t^{2} + 3 t + 7)

化简

(2 t + 3) (3 t^{2} + 3) + 6 t (t^{2} + 3 t + 7) : 12 t^{3} + 27 t^{2} + 48 t + 9

= 12 t^{3} + 27 t^{2} + 48 t + 9

\int \frac{1}{x ^{2} 81 - x ^{2}} d x

\int x^{3} e^{3 x^{2}} d x

y^{^{''}} - 3 y^{^{'}} + 2 y = t

\frac{d}{d y} (sin (x + y))

x \to π lim (x^{3} cos (x))