What is (\partial)/(\partial x)(ln(1+xy)) ?

The answer to (\partial)/(\partial x)(ln(1+xy)) is y/(1+xy)

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(\partial)/(\partial x)(ln(1+xy))

\frac{\partial}{\partial x} (ln (1 + x y))

\frac{y}{1 + x y}

Solution steps

\frac{\partial}{\partial x} (ln (1 + x y))

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{1 + x y} y : \frac{y}{1 + x y}

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

f (x) = \frac{2 x + 3}{3 x + 2}

\frac{\partial}{\partial x} ((e^{x - y}) g oo g)

f (x) = 1 - 2 cos (x)

\frac{d}{d x} ((\frac{x - 5}{x + 5})^{4})

\int \frac{x ^{3}}{x ^{2} - x - 2} d x

What is (\partial)/(\partial x)(ln(1+xy)) ?
The answer to (\partial)/(\partial x)(ln(1+xy)) is y/(1+xy)