derivative G(t)=(4t)/(t+5)

解答

导数

G (t) = \frac{4 t}{t + 5}

\frac{20}{( t + 5 ) ^{2}}

求解步骤

\frac{d}{d t} (\frac{4 t}{t + 5})

将常数提出:

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

= 4 \frac{d}{d t} (\frac{t}{t + 5})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 4 \cdot \frac{\frac{d t}{d t} ( t + 5 ) - \frac{d}{d t} ( t + 5 ) t}{( t + 5 ) ^{2}}

\frac{d t}{d t} = 1

\frac{d}{d t} (t + 5) = 1

= 4 \cdot \frac{1 \cdot ( t + 5 ) - 1 \cdot t}{( t + 5 ) ^{2}}

化简

4 \cdot \frac{1 \cdot ( t + 5 ) - 1 \cdot t}{( t + 5 ) ^{2}} : \frac{20}{( t + 5 ) ^{2}}

= \frac{20}{( t + 5 ) ^{2}}