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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= k \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}}

= k \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}

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

Simplify

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

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

f (x) = (5 x + 4)^{2}

f (t) = \frac{t ^{2} - 1}{( t ^{2} + t - 2 )}

5 x - 1

cos^{2} (5 x^{2} + 6 x + 5)

\frac{4 x ^{3}}{3 - x}

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