What is (\partial)/(\partial r)(1/(r^2)) ?

The answer to (\partial)/(\partial r)(1/(r^2)) is -2/(r^3)

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(\partial)/(\partial r)(1/(r^2))

\frac{\partial}{\partial r} (\frac{1}{r ^{2}})

- \frac{2}{r ^{3}}

Solution steps

\frac{\partial}{\partial r} (\frac{1}{r ^{2}})

Apply exponent rule:

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

= \frac{\partial}{\partial r} (r^{- 2})

Apply the Power Rule:

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

= - 2 r^{- 2 - 1}

Simplify

- 2 r^{- 2 - 1} : - \frac{2}{r ^{3}}

= - \frac{2}{r ^{3}}

\frac{d}{d x} (\frac{128}{( 1 + 4 x ) ^{3}})

\frac{d ^{2}}{d x ^{2}} (∣ x ∣)

\frac{d}{d t} (t e^{- 3 t})

\frac{d}{d x} (\frac{6 ( x ^{2} + 1 )}{( x ^{2} - 3 ) ^{3}})

What is (\partial)/(\partial r)(1/(r^2)) ?
The answer to (\partial)/(\partial r)(1/(r^2)) is -2/(r^3)