derivative 3sin(t)cos(t)

解答

导数

3 sin (t) cos (t)

3 cos (2 t)

求解步骤

\frac{d}{d t} (3 sin (t) cos (t))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d t} (sin (t) cos (t))

使用微分乘法定则:

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

f = sin (t), g = cos (t)

= 3 (\frac{d}{d t} (sin (t)) cos (t) + \frac{d}{d t} (cos (t)) sin (t))

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

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

= 3 (cos (t) cos (t) + (- sin (t)) sin (t))

化简

3 (cos (t) cos (t) + (- sin (t)) sin (t)) : 3 cos (2 t)

= 3 cos (2 t)

n = 1 \sum \infty (0.2)^{n}

\int_{\frac{π}{2}}^{π} cos^{2} (x) d x

2 y^{^{''}} + 18 y = 0

\int \frac{x}{( 3 - x ^{2} ) ^{6}} d x

\frac{\partial}{\partial x} (5 + x ln (x y - 5))