What is (\partial)/(\partial x)(5/x) ?

The answer to (\partial)/(\partial x)(5/x) is -5/(x^2)

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(\partial)/(\partial x)(5/x)

\frac{\partial}{\partial x} (\frac{5}{x})

- \frac{5}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{5}{x})

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= 5 \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= 5 (- 1 \cdot x^{- 1 - 1})

Simplify

5 (- 1 \cdot x^{- 1 - 1}) : - \frac{5}{x ^{2}}

= - \frac{5}{x ^{2}}

x \to 0 lim ((\frac{1}{2})^{x})

\frac{d}{d t} (C e^{3 t} - e^{2})

x \to 0 lim (- \frac{1}{2 ( 2 + x )})

n = 1 \sum \infty (- 1)^{n} n! x^{n}

\frac{1}{2 t + 4 i} + 2 j

What is (\partial)/(\partial x)(5/x) ?
The answer to (\partial)/(\partial x)(5/x) is -5/(x^2)