What is (\partial)/(\partial x)(-1/(ax^2)) ?

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

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(\partial)/(\partial x)(-1/(ax^2))

\frac{\partial}{\partial x} (- \frac{1}{a x ^{2}})

\frac{2}{a x ^{3}}

Solution steps

\frac{\partial}{\partial x} (- \frac{1}{a x ^{2}})

Take the constant out:

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

= - \frac{1}{a} \frac{\partial}{\partial x} (\frac{1}{x ^{2}})

Apply exponent rule:

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

= - \frac{1}{a} \frac{\partial}{\partial x} (x^{- 2})

Apply the Power Rule:

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

= - \frac{1}{a} (- 2 x^{- 2 - 1})

Simplify

- \frac{1}{a} (- 2 x^{- 2 - 1}) : \frac{2}{a x ^{3}}

= \frac{2}{a x ^{3}}

x = 18.432 t cos (1.44 t^{2})

\frac{d}{d x} y = x^{2} 2^{x} + π^{2} + x^{e}

\frac{d}{d y} (\frac{y}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}})

\int cos (x) - 5 sin (x) - 7 d x

\frac{d}{d t} (e^{2 t} + 2 e^{t} + 1)

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