What is (\partial)/(\partial x)(1/(x^3)) ?

The answer to (\partial)/(\partial x)(1/(x^3)) is -3/(x^4)

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(\partial)/(\partial x)(1/(x^3))

\frac{\partial}{\partial x} (\frac{1}{x ^{3}})

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

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= \frac{\partial}{\partial x} (x^{- 3})

Apply the Power Rule:

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

= - 3 x^{- 3 - 1}

Simplify

- 3 x^{- 3 - 1} : - \frac{3}{x ^{4}}

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

\frac{d}{d x} (5^{c o s (x)})

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

x \to \frac{8}{9} lim (x^{4})

f (t) = 5 cos (t)

\frac{d y}{d x} = 8 x (6 y + 5)^{\frac{1}{2}}

What is (\partial)/(\partial x)(1/(x^3)) ?
The answer to (\partial)/(\partial x)(1/(x^3)) is -3/(x^4)