What is (\partial)/(\partial x)(((5x+3))/(y-2)) ?

The answer to (\partial)/(\partial x)(((5x+3))/(y-2)) is 5/(y-2)

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(\partial)/(\partial x)(((5x+3))/(y-2))

\frac{\partial}{\partial x} (\frac{( 5 x + 3 )}{y - 2})

\frac{5}{y - 2}

Solution steps

\frac{\partial}{\partial x} (\frac{( 5 x + 3 )}{y - 2})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{y - 2} \frac{\partial}{\partial x} (5 x + 3)

Apply the Sum/Difference Rule:

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

= \frac{1}{y - 2} (\frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (3))

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

\frac{\partial}{\partial x} (3) = 0

= \frac{1}{y - 2} (5 + 0)

Simplify

\frac{1}{y - 2} (5 + 0) : \frac{5}{y - 2}

= \frac{5}{y - 2}

What is (\partial)/(\partial x)(((5x+3))/(y-2)) ?
The answer to (\partial)/(\partial x)(((5x+3))/(y-2)) is 5/(y-2)