d/(dq)((q^1q^2)/(r^2))

解答

\frac{d}{d q} (\frac{q ^{1} q ^{2}}{r ( q ) ^{2}})

\frac{q ^{2} ( - 2 q \frac{d r}{d q} + 3 r )}{r ^{3}}

求解步骤

\frac{d}{d q} (\frac{q ^{1} q ^{2}}{r ^{2}})

使用微分除法定则:

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

= \frac{\frac{d}{d q} ( q ^{1} q ^{2} ) r ^{2} - \frac{d}{d q} ( r ^{2} ) q ^{1} q ^{2}}{( r ^{2} ) ^{2}}

\frac{d}{d q} (q^{1} q^{2}) = 3 q^{2}

\frac{d}{d q} (r^{2}) = 2 r \frac{d r}{d q}

= \frac{3 q ^{2} r ^{2} - 2 r \frac{d r}{d q} q ^{1} q ^{2}}{( r ^{2} ) ^{2}}

化简

\frac{3 q ^{2} r ^{2} - 2 r \frac{d r}{d q} q ^{1} q ^{2}}{( r ^{2} ) ^{2}} : \frac{q ^{2} ( - 2 q \frac{d r}{d q} + 3 r )}{r ^{3}}

= \frac{q ^{2} ( - 2 q \frac{d r}{d q} + 3 r )}{r ^{3}}

d er i v a t i v e \frac{x + 4}{x}

d er i v a t i v e y = (x^{2} + 3)^{7}

d er i v a t i v e \frac{5}{1 - x}

d er i v a t i v e (1 + x)^{\frac{1}{2}}

\frac{d}{d t} (a \cdot e^{- 9 t} \cdot cos (3 t + b))