What is (\partial)/(\partial x)((5x+8)/(4y+1)) ?

The answer to (\partial)/(\partial x)((5x+8)/(4y+1)) is 5/(4y+1)

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(\partial)/(\partial x)((5x+8)/(4y+1))

\frac{\partial}{\partial x} (\frac{5 x + 8}{4 y + 1})

\frac{5}{4 y + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{5 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} (5 x + 8)

Apply the Sum/Difference Rule:

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

= \frac{1}{4 y + 1} (\frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (8))

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

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

= \frac{1}{4 y + 1} (5 + 0)

Simplify

\frac{1}{4 y + 1} (5 + 0) : \frac{5}{4 y + 1}

= \frac{5}{4 y + 1}

f (x) = (4 x)

\int_{0}^{2 π} sin^{2} (6 x) d x

x \to 3 lim (lo g_{3} (x))

3 x - 8 y x^{2} + 1 (\frac{d y}{d x}) = 0

What is (\partial)/(\partial x)((5x+8)/(4y+1)) ?
The answer to (\partial)/(\partial x)((5x+8)/(4y+1)) is 5/(4y+1)