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

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

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(\partial)/(\partial x)(ln(x^2y))

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

\frac{2}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{x}

x \to 0 lim (x sin (\frac{3 π}{x}))

y = - \frac{14}{x ^{5}}

\frac{\partial}{\partial x} (6 x^{3} cos (6 x^{2} y))

y = x^{2}, y = 3

\int_{0}^{\frac{π}{4}} sec^{2} (x) d x

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