What is (\partial)/(\partial x)(1/(x^4)) ?

The answer to (\partial)/(\partial x)(1/(x^4)) is -4/(x^5)

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(\partial)/(\partial x)(1/(x^4))

\frac{\partial}{\partial x} (\frac{1}{x ^{4}})

- \frac{4}{x ^{5}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x ^{4}})

Apply exponent rule:

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

= \frac{\partial}{\partial x} (x^{- 4})

Apply the Power Rule:

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

= - 4 x^{- 4 - 1}

Simplify

- 4 x^{- 4 - 1} : - \frac{4}{x ^{5}}

= - \frac{4}{x ^{5}}

e^{x} (y - 1) d x + 2 (e^{x} + 4) d y = 0

x, 4

\frac{3}{x ^{4} + 7 x + 1}

y^{^{'}} = 3 x y

\frac{7 + 2 x}{1 - 6 x}

What is (\partial)/(\partial x)(1/(x^4)) ?
The answer to (\partial)/(\partial x)(1/(x^4)) is -4/(x^5)