What is (\partial)/(\partial x)((4x+9)/(3y+1)) ?

The answer to (\partial)/(\partial x)((4x+9)/(3y+1)) is 4/(3y+1)

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(\partial)/(\partial x)((4x+9)/(3y+1))

\frac{\partial}{\partial x} (\frac{4 x + 9}{3 y + 1})

\frac{4}{3 y + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{4 x + 9}{3 y + 1})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{3 y + 1} \frac{\partial}{\partial x} (4 x + 9)

Apply the Sum/Difference Rule:

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

= \frac{1}{3 y + 1} (\frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (9))

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

\frac{\partial}{\partial x} (9) = 0

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

Simplify

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

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

f (x) = 4 x^{2} + 5 x + 3

\int (x^{3} + 3 x)^{32} (3 x^{2} + 3) d x

x \to \infty lim (1 + \frac{1}{x})

x x^{2} + 5

n = 2 \sum \infty \frac{1}{n}

What is (\partial)/(\partial x)((4x+9)/(3y+1)) ?
The answer to (\partial)/(\partial x)((4x+9)/(3y+1)) is 4/(3y+1)