What is (\partial}{\partial {h}}(A/({h)+sqrt(5)/h)) ?

The answer to (\partial}{\partial {h}}(A/({h)+sqrt(5)/h)) is ((1-sqrt(5))A)/(4{h)^2}

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(\partial}{\partial {h}}(A/({h)+sqrt(5)/h))

\frac{\partial}{\partial h} (\frac{A}{h + 5 h})

\frac{( 1 - 5 ) A}{4 h ^{2}}

Solution steps

\frac{\partial}{\partial h} (\frac{A}{h + 5 h})

Simplify

\frac{A}{h + 5 h} : - \frac{( 1 - 5 ) A}{4 h}

= \frac{\partial}{\partial h} (- \frac{( 1 - 5 ) A}{4 h})

Take the constant out:

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

= - \frac{( 1 - 5 ) A}{4} \frac{\partial}{\partial h} (\frac{1}{h})

Apply exponent rule:

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

= - \frac{( 1 - 5 ) A}{4} \frac{\partial}{\partial h} (h^{- 1})

Apply the Power Rule:

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

= - \frac{( 1 - 5 ) A}{4} (- 1 \cdot h^{- 1 - 1})

Simplify

- \frac{( 1 - 5 ) A}{4} (- 1 \cdot h^{- 1 - 1}) : \frac{( 1 - 5 ) A}{4 h ^{2}}

= \frac{( 1 - 5 ) A}{4 h ^{2}}

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What is (\partial}{\partial {h}}(A/({h)+sqrt(5)/h)) ?
The answer to (\partial}{\partial {h}}(A/({h)+sqrt(5)/h)) is ((1-sqrt(5))A)/(4{h)^2}