What is the first d/(da)(a/(b-3)) ?

The first d/(da)(a/(b-3)) is 1/(b-3)

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d/(da)(a/(b-3))

\frac{d}{d a} (\frac{a}{b - 3})

\frac{1}{b - 3}

Solution steps

\frac{d}{d a} (\frac{a}{b - 3})

Take the constant out:

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

= \frac{1}{b - 3} \frac{d a}{d a}

Apply the common derivative:

\frac{d a}{d a} = 1

= \frac{1}{b - 3} \cdot 1

Simplify

= \frac{1}{b - 3}