What is (\partial)/(\partial x)(((3x+8))/(4y+1)) ?

The answer to (\partial)/(\partial x)(((3x+8))/(4y+1)) is 3/(4y+1)

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(\partial)/(\partial x)(((3x+8))/(4y+1))

\frac{\partial}{\partial x} (\frac{( 3 x + 8 )}{4 y + 1})

\frac{3}{4 y + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{( 3 x + 8 )}{4 y + 1})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{4 y + 1} \frac{\partial}{\partial x} (3 x + 8)

Apply the Sum/Difference Rule:

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

= \frac{1}{4 y + 1} (\frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (8))

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

\frac{\partial}{\partial x} (8) = 0

= \frac{1}{4 y + 1} (3 + 0)

Simplify

\frac{1}{4 y + 1} (3 + 0) : \frac{3}{4 y + 1}

= \frac{3}{4 y + 1}

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What is (\partial)/(\partial x)(((3x+8))/(4y+1)) ?
The answer to (\partial)/(\partial x)(((3x+8))/(4y+1)) is 3/(4y+1)