What is the d/(d{r)}(({g}*(m_{1}*m_{2}))/(({r)^2)}) ?

The d/(d{r)}(({g}*(m_{1}*m_{2}))/(({r)^2)}) is -(2m_{1}m_{2)/g}{{r}^3}

What is the first d/(d{r)}(({g}*(m_{1}*m_{2}))/(({r)^2)}) ?

The first d/(d{r)}(({g}*(m_{1}*m_{2}))/(({r)^2)}) is -(2m_{1}m_{2)/g}{{r}^3}

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\frac{d}{d r} (\frac{g \cdot ( m _{1} \cdot m _{2} )}{( r ^{2} )})

- \frac{2 m _{1} m _{2} g}{r ^{3}}

Solution steps

\frac{d}{d r} (\frac{g ( m _{1} m _{2} )}{( r ^{2} )})

Take the constant out:

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

= g m_{1} m_{2} \frac{d}{d r} (\frac{1}{r ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= g m_{1} m_{2} (- 2 r^{- 2 - 1})

Simplify

g m_{1} m_{2} (- 2 r^{- 2 - 1}) : - \frac{2 m _{1} m _{2} g}{r ^{3}}

= - \frac{2 m _{1} m _{2} g}{r ^{3}}

What is the d/(d{r)}(({g}*(m_{1}*m_{2}))/(({r)^2)}) ?
The d/(d{r)}(({g}*(m_{1}*m_{2}))/(({r)^2)}) is -(2m_{1}m_{2)/g}{{r}^3}
What is the first d/(d{r)}(({g}*(m_{1}*m_{2}))/(({r)^2)}) ?
The first d/(d{r)}(({g}*(m_{1}*m_{2}))/(({r)^2)}) is -(2m_{1}m_{2)/g}{{r}^3}