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

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

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

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

\frac{2}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{2} y} \cdot 4 y x

Simplify

\frac{1}{2 x ^{2} y} \cdot 4 y x : \frac{2}{x}

= \frac{2}{x}

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

y = 25 - x^{2}

x + 1, 0

\int k e^{x} d x

n = 1 \sum \infty n \cdot e^{- n^{2}}

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