What is (\partial)/(\partial x)((ax-5)/(-y^2+1)) ?

The answer to (\partial)/(\partial x)((ax-5)/(-y^2+1)) is a/(-y^2+1)

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(\partial)/(\partial x)((ax-5)/(-y^2+1))

\frac{\partial}{\partial x} (\frac{a x - 5}{- y ^{2} + 1})

\frac{a}{- y ^{2} + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{a x - 5}{- y ^{2} + 1})

Treat

a, y

as a constant

Take the constant out:

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

= \frac{1}{- y ^{2} + 1} \frac{\partial}{\partial x} (a x - 5)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{- y ^{2} + 1} (\frac{\partial}{\partial x} (a x) - \frac{\partial}{\partial x} (5))

\frac{\partial}{\partial x} (a x) = a

\frac{\partial}{\partial x} (5) = 0

= \frac{1}{- y ^{2} + 1} (a - 0)

Simplify

\frac{1}{- y ^{2} + 1} (a - 0) : \frac{a}{- y ^{2} + 1}

= \frac{a}{- y ^{2} + 1}

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What is (\partial)/(\partial x)((ax-5)/(-y^2+1)) ?
The answer to (\partial)/(\partial x)((ax-5)/(-y^2+1)) is a/(-y^2+1)