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

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

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

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

\frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

\frac{\partial}{\partial x} (e^{- x} sin (x^{2} + x y))

\frac{\partial}{\partial u} (u^{2} - v^{2})

\int csc^{2} (\frac{1}{3}) x d x

\frac{1}{1 + t}

\frac{2 x}{x ^{4} + 1}

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