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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derivative of

\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}}

\frac{s}{( s - 1 )}

y (1 + x^{2}) y^{^{'}} - x (6 + y^{2}) = 0

y = 5 x^{4} e^{x} + e^{x} x^{5}

x \to 1 lim (- 6 + 2 x^{2})

f (x) = \frac{x + 2}{x ^{2}}