What is the d/(dq)((q^1q^2)/(r^2)) ?

The d/(dq)((q^1q^2)/(r^2)) is (q^2(-2q\frac{dr)/(dq)+3r)}{r^3}

What is the first d/(dq)((q^1q^2)/(r^2)) ?

The first d/(dq)((q^1q^2)/(r^2)) is (q^2(-2q\frac{dr)/(dq)+3r)}{r^3}

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\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}}

Solution steps

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

Apply the Quotient Rule:

(\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}}

Simplify

\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}}

What is the d/(dq)((q^1q^2)/(r^2)) ?
The d/(dq)((q^1q^2)/(r^2)) is (q^2(-2q\frac{dr)/(dq)+3r)}{r^3}
What is the first d/(dq)((q^1q^2)/(r^2)) ?
The first d/(dq)((q^1q^2)/(r^2)) is (q^2(-2q\frac{dr)/(dq)+3r)}{r^3}