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

The answer to (\partial)/(\partial y)(ln(x^2y)) is 1/y

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

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

\frac{1}{y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{y}

7 \cdot ln (x)

sin^{3} (3 x)

\frac{\partial}{\partial y} (- 2 cos (y))

\frac{\partial}{\partial x} (x^{4} - y^{2})

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 3})

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