What is (\partial)/(\partial x)((x^2+4)/(y-3)) ?

The answer to (\partial)/(\partial x)((x^2+4)/(y-3)) is (2x)/(y-3)

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(\partial)/(\partial x)((x^2+4)/(y-3))

\frac{\partial}{\partial x} (\frac{x ^{2} + 4}{y - 3})

\frac{2 x}{y - 3}

Solution steps

\frac{\partial}{\partial x} (\frac{x ^{2} + 4}{y - 3})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{y - 3} \frac{\partial}{\partial x} (x^{2} + 4)

Apply the Sum/Difference Rule:

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

= \frac{1}{y - 3} (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (4))

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (4) = 0

= \frac{1}{y - 3} (2 x + 0)

Simplify

\frac{1}{y - 3} (2 x + 0) : \frac{2 x}{y - 3}

= \frac{2 x}{y - 3}

y^{^{'}} = \frac{y ^{2} - y}{x}

x + 2, x^{2}, - 1, 2

y = \frac{x}{3 + x}

\int - \frac{3}{x ^{3}} d x

\frac{d}{d x} (arcsin (x^{2} - 3))

What is (\partial)/(\partial x)((x^2+4)/(y-3)) ?
The answer to (\partial)/(\partial x)((x^2+4)/(y-3)) is (2x)/(y-3)