d/(dt)((x)(t+sqrt(t)))

解答

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

\frac{d x}{d t} (t + t) + (1 + \frac{1}{2 t}) x

求解步骤

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

使用微分乘法定则:

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

f = x, g = t + t

= \frac{d x}{d t} (t + t) + \frac{d}{d t} (t + t) x

\frac{d}{d t} (t + t) = 1 + \frac{1}{2 t}

= \frac{d x}{d t} (t + t) + (1 + \frac{1}{2 t}) x

s im pl i f y (- a - x) (a + x)

e x p an d (2 e^{2 t} + 2)^{2}

e x p an d (e^{y} - y e^{y}) d y

e x p an d \frac{( 1 - 3 t ) ( - 27 t e ^{- t} - 11 t - 8 )}{9}

s im pl i f y (\frac{1}{24} sin (10 x) - \frac{5}{24} (sin (2 x))) cos (6 x)