derivative (470t)/((t^2+6)^3)

解答

导数

\frac{470 t}{( t ^{2} + 6 ) ^{3}}

\frac{470 ( - 5 t ^{2} + 6 )}{( t ^{2} + 6 ) ^{4}}

求解步骤

\frac{d}{d t} (\frac{470 t}{( t ^{2} + 6 ) ^{3}})

将常数提出:

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

= 470 \frac{d}{d t} (\frac{t}{( t ^{2} + 6 ) ^{3}})

使用微分除法定则:

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

= 470 \cdot \frac{\frac{d t}{d t} ( t ^{2} + 6 ) ^{3} - \frac{d}{d t} ( ( t ^{2} + 6 ) ^{3} ) t}{( ( t ^{2} + 6 ) ^{3} ) ^{2}}

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

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

= 470 \cdot \frac{1 \cdot ( t ^{2} + 6 ) ^{3} - 6 t ( t ^{2} + 6 ) ^{2} t}{( ( t ^{2} + 6 ) ^{3} ) ^{2}}

化简

470 \cdot \frac{1 \cdot ( t ^{2} + 6 ) ^{3} - 6 t ( t ^{2} + 6 ) ^{2} t}{( ( t ^{2} + 6 ) ^{3} ) ^{2}} : \frac{470 ( - 5 t ^{2} + 6 )}{( t ^{2} + 6 ) ^{4}}

= \frac{470 ( - 5 t ^{2} + 6 )}{( t ^{2} + 6 ) ^{4}}

y^{^{''}} - 6 y^{^{'}} + 8 y = - 4 e^{3 t}

\frac{\partial ^{2}}{\partial y ^{2}} (2 cos (x y^{2}))

t an g e n t f (x) = 4 x^{2} - 5 x, at x = - 3

\frac{\partial}{\partial x} (x^{2} ln (y - 1))

\int_{1}^{2} x (x - 1)^{4} d x