What is (\partial)/(\partial x)(log_{e}(x+y)) ?

The answer to (\partial)/(\partial x)(log_{e}(x+y)) is 1/(x+y)

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(\partial)/(\partial x)(log_{e}(x+y))

\frac{\partial}{\partial x} (lo g_{e} (x + y))

\frac{1}{x + y}

Solution steps

\frac{\partial}{\partial x} (lo g_{e} (x + y))

Simplify

lo g_{e} (x + y) : ln (x + y)

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= \frac{1}{x + y}

f (x) = 5^{x}

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

y^{^{'}} - x y = x y^{\frac{3}{2}}

\frac{1}{x}

y = 9 arctan (x - 1 + x^{2})

What is (\partial)/(\partial x)(log_{e}(x+y)) ?
The answer to (\partial)/(\partial x)(log_{e}(x+y)) is 1/(x+y)