What is (\partial}{\partial x}(ln(\frac{y^2)/x)) ?

The answer to (\partial}{\partial x}(ln(\frac{y^2)/x)) is -1/x

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(\partial}{\partial x}(ln(\frac{y^2)/x))

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

- \frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{\frac{y ^{2}}{x}} (- \frac{y ^{2}}{x ^{2}})

Simplify

\frac{1}{\frac{y ^{2}}{x}} (- \frac{y ^{2}}{x ^{2}}) : - \frac{1}{x}

= - \frac{1}{x}

(x - 4)^{3} + 3 x (x - 4)^{2}

x \to - \infty lim (x^{6})

\frac{\partial}{\partial x} (- 4 cos (3 x))

\int \frac{12 s + 12}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

\int \frac{1}{4 - x ^{2}} d x

What is (\partial}{\partial x}(ln(\frac{y^2)/x)) ?
The answer to (\partial}{\partial x}(ln(\frac{y^2)/x)) is -1/x