What is the derivative of h/x ?

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

What is the first derivative of h/x ?

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

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\frac{d}{d x} (\frac{h}{x})

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

Solution steps

\frac{d}{d x} (\frac{h}{x})

Treat

h

as a constant

Take the constant out:

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

= h \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{1}{( ( s ^{2} + 3 s + 2 ) ( s + 1 ) )}

\frac{d}{d x} (6 e^{x^{2}} x)

y^{^{'}} = y^{2} sin (x)

\int_{1}^{4} \frac{1}{x + 2 x} d x

\frac{d}{d x} (\frac{e ^{- x}}{2})