derivative ((t^3)/(t^8+7))^2

解答

导数

(\frac{t ^{3}}{t ^{8} + 7})^{2}

\frac{2 t ^{3} ( - 5 t ^{10} + 21 t ^{2} )}{( t ^{8} + 7 ) ^{3}}

求解步骤

\frac{d}{d t} ((\frac{t ^{3}}{t ^{8} + 7})^{2})

使用连锁律:

2 \cdot \frac{t ^{3}}{t ^{8} + 7} \frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 7})

= 2 \cdot \frac{t ^{3}}{t ^{8} + 7} \frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 7})

\frac{d}{d t} (\frac{t ^{3}}{t ^{8} + 7}) = \frac{- 5 t ^{10} + 21 t ^{2}}{( t ^{8} + 7 ) ^{2}}

= 2 \cdot \frac{t ^{3}}{t ^{8} + 7} \cdot \frac{- 5 t ^{10} + 21 t ^{2}}{( t ^{8} + 7 ) ^{2}}

化简

2 \cdot \frac{t ^{3}}{t ^{8} + 7} \cdot \frac{- 5 t ^{10} + 21 t ^{2}}{( t ^{8} + 7 ) ^{2}} : \frac{2 t ^{3} ( - 5 t ^{10} + 21 t ^{2} )}{( t ^{8} + 7 ) ^{3}}

= \frac{2 t ^{3} ( - 5 t ^{10} + 21 t ^{2} )}{( t ^{8} + 7 ) ^{3}}

\int (x + 1) ln (2 x + 4) d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) (x + 7 x^{3}))

\frac{d y}{d x} = x (9 - y)

\frac{d}{d x} (\frac{1 + 3 x}{1 - 3 x})

x \to \infty lim (9)