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

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

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

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

\frac{2}{x}

Solution steps

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

Simplify

ln (x y) + ln (\frac{x}{y}) : ln (x^{2})

= \frac{\partial}{\partial x} (ln (x^{2}))

Apply the chain rule:

\frac{1}{x ^{2}} \frac{\partial}{\partial x} (x^{2})

= \frac{1}{x ^{2}} \frac{\partial}{\partial x} (x^{2})

\frac{\partial}{\partial x} (x^{2}) = 2 x

= \frac{1}{x ^{2}} \cdot 2 x

Simplify

\frac{1}{x ^{2}} \cdot 2 x : \frac{2}{x}

= \frac{2}{x}

\int (e^{2 y}) d y

\frac{d}{d x} (7^{x^{4} + 2 x})

f (x) = 2 x^{4} - 16 x^{3} + 9

\int \frac{ln ^{2} ( x )}{x ^{3}} d x

y = sin (2 x), at x = \frac{3 π}{4}

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