What is the derivative of-a/x ?

The derivative of-a/x is a/(x^2)

What is the first derivative of-a/x ?

The first derivative of-a/x is a/(x^2)

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

\frac{a}{x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{a}{x ^{2}}

\int \frac{e ^{x}}{1 + e ^{x}} d x

\int x^{9} x^{5} + 3 d x

\frac{d}{d x} (ln ((5 x)^{2}))

y^{^{''}} + 7 y^{^{'}} = 0

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