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

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

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

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

\frac{2 x}{x ^{2} + 2 y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = \frac{y}{( 1 + x ) ( 2 + x )}

\frac{d}{d x} (\frac{x ^{2}}{4 - x ^{2}})

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

\frac{\partial}{\partial x} (40 x)

ln (8 x)

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