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}}

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

\int sec^{2} (x t a) n^{6} x d x

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

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)