What is (\partial)/(\partial x)(((5x+4))/(5y+1)) ?

The answer to (\partial)/(\partial x)(((5x+4))/(5y+1)) is 5/(5y+1)

(\partial)/(\partial x)(((5x+4))/(5y+1))

\frac{\partial}{\partial x} (\frac{( 5 x + 4 )}{5 y + 1})

\frac{5}{5 y + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{( 5 x + 4 )}{5 y + 1})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{5 y + 1} \frac{\partial}{\partial x} (5 x + 4)

Apply the Sum/Difference Rule:

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

= \frac{1}{5 y + 1} (\frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (4))

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

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

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

Simplify

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

= \frac{5}{5 y + 1}

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What is (\partial)/(\partial x)(((5x+4))/(5y+1)) ?
The answer to (\partial)/(\partial x)(((5x+4))/(5y+1)) is 5/(5y+1)