What is (\partial)/(\partial x)(ln(2xy+4)) ?

The answer to (\partial)/(\partial x)(ln(2xy+4)) is y/(xy+2)

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(\partial)/(\partial x)(ln(2xy+4))

\frac{\partial}{\partial x} (ln (2 x y + 4))

\frac{y}{x y + 2}

Solution steps

\frac{\partial}{\partial x} (ln (2 x y + 4))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x y + 4} \frac{\partial}{\partial x} (2 x y + 4)

= \frac{1}{2 x y + 4} \frac{\partial}{\partial x} (2 x y + 4)

\frac{\partial}{\partial x} (2 x y + 4) = 2 y

= \frac{1}{2 x y + 4} \cdot 2 y

Simplify

\frac{1}{2 x y + 4} \cdot 2 y : \frac{y}{x y + 2}

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

\frac{\partial}{\partial y} (arctan (x + 6 y))

y = x^{2} + 3

\int_{1}^{4} \frac{7}{x ^{2}} d x

(9 x + 3) + (9 y - 9) y^{^{'}} = 0

\int_{0}^{3} (x + 9 - x^{2}) d x

What is (\partial)/(\partial x)(ln(2xy+4)) ?
The answer to (\partial)/(\partial x)(ln(2xy+4)) is y/(xy+2)