What is the d/(dh)((e^{ah}-1)/h) ?

The d/(dh)((e^{ah}-1)/h) is (ae^{ah}h-e^{ah}+1)/(h^2)

What is the first d/(dh)((e^{ah}-1)/h) ?

The first d/(dh)((e^{ah}-1)/h) is (ae^{ah}h-e^{ah}+1)/(h^2)

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\frac{d}{d h} (\frac{e ^{ah} - 1}{h})

\frac{a e ^{ah} h - e ^{ah} + 1}{h ^{2}}

Solution steps

\frac{d}{d h} (\frac{e ^{ah} - 1}{h})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d h} ( e ^{ah} - 1 ) h - \frac{d h}{d h} ( e ^{ah} - 1 )}{h ^{2}}

\frac{d}{d h} (e^{ah} - 1) = a e^{ah}

\frac{d h}{d h} = 1

= \frac{a e ^{ah} h - 1 \cdot ( e ^{ah} - 1 )}{h ^{2}}

Simplify

= \frac{a e ^{ah} h - e ^{ah} + 1}{h ^{2}}

What is the d/(dh)((e^{ah}-1)/h) ?
The d/(dh)((e^{ah}-1)/h) is (ae^{ah}h-e^{ah}+1)/(h^2)
What is the first d/(dh)((e^{ah}-1)/h) ?
The first d/(dh)((e^{ah}-1)/h) is (ae^{ah}h-e^{ah}+1)/(h^2)