derivative (t+1)cos(-t)

解答

导数

(t + 1) cos (- t)

- sin (t) (1 + t) + cos (t)

求解步骤

\frac{d}{d t} ((t + 1) cos (- t))

化简

(t + 1) cos (- t) : cos (t) (1 + t)

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

使用微分乘法定则:

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

f = cos (t), g = 1 + t

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

\frac{d}{d t} (cos (t)) = - sin (t)

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

= (- sin (t)) (1 + t) + 1 \cdot cos (t)

化简

= - sin (t) (1 + t) + cos (t)

\int - 2 cos^{2} (x) sin (x) d x

\frac{d v}{d t} = 32 - \frac{4}{5} v

\frac{\partial}{\partial x} (x^{5} y^{5} + 4 x^{7} y)

\int \frac{1}{( x - 5 ) ^{\frac{3}{2}}} d x

x y^{^{'}} + (1 + 2 x) y = 10 e^{- 2 x}