What is (\partial)/(\partial x)((2x+7)/(2y+1)) ?

The answer to (\partial)/(\partial x)((2x+7)/(2y+1)) is 2/(2y+1)

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(\partial)/(\partial x)((2x+7)/(2y+1))

\frac{\partial}{\partial x} (\frac{2 x + 7}{2 y + 1})

\frac{2}{2 y + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{2 x + 7}{2 y + 1})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{2 y + 1} \frac{\partial}{\partial x} (2 x + 7)

Apply the Sum/Difference Rule:

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

= \frac{1}{2 y + 1} (\frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (7))

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

\frac{\partial}{\partial x} (7) = 0

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

Simplify

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

= \frac{2}{2 y + 1}

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\int 7 sin (5 θ) sin (θ) d θ

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What is (\partial)/(\partial x)((2x+7)/(2y+1)) ?
The answer to (\partial)/(\partial x)((2x+7)/(2y+1)) is 2/(2y+1)