What is (\partial)/(\partial x)(6/(x^3)) ?

The answer to (\partial)/(\partial x)(6/(x^3)) is -(18)/(x^4)

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(\partial)/(\partial x)(6/(x^3))

\frac{\partial}{\partial x} (\frac{6}{x ^{3}})

- \frac{18}{x ^{4}}

Solution steps

\frac{\partial}{\partial x} (\frac{6}{x ^{3}})

Take the constant out:

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

= 6 \frac{\partial}{\partial x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= 6 \frac{\partial}{\partial x} (x^{- 3})

Apply the Power Rule:

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

= 6 (- 3 x^{- 3 - 1})

Simplify

6 (- 3 x^{- 3 - 1}) : - \frac{18}{x ^{4}}

= - \frac{18}{x ^{4}}

\frac{d}{d x} (\frac{20}{x ^{3}})

\int 3 x^{2} - 5 x + 2 d x

\int_{0}^{\infty} 6 e^{- 3 x} d x

\frac{d}{d x} (\frac{x - 19}{x - 19})

f (x) = x^{4} - 13 x^{2} + 36, at x = 1

What is (\partial)/(\partial x)(6/(x^3)) ?
The answer to (\partial)/(\partial x)(6/(x^3)) is -(18)/(x^4)