What is (\partial)/(\partial x)(1/(x^7)) ?

The answer to (\partial)/(\partial x)(1/(x^7)) is -7/(x^8)

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(\partial)/(\partial x)(1/(x^7))

\frac{\partial}{\partial x} (\frac{1}{x ^{7}})

- \frac{7}{x ^{8}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x ^{7}})

Apply exponent rule:

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

= \frac{\partial}{\partial x} (x^{- 7})

Apply the Power Rule:

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

= - 7 x^{- 7 - 1}

Simplify

- 7 x^{- 7 - 1} : - \frac{7}{x ^{8}}

= - \frac{7}{x ^{8}}

\int cos^{2} (5 y) sin (5 y) d y

\int_{- 3}^{\infty} e^{- x} d x

\frac{1}{1 - x}

\frac{\partial}{\partial z} (- 9 z cos (3 x + yz))

\frac{d}{d x} (1 + x^{2} + y^{2})

What is (\partial)/(\partial x)(1/(x^7)) ?
The answer to (\partial)/(\partial x)(1/(x^7)) is -7/(x^8)