What is (\partial)/(\partial x)(ln(1+x^2+y^2)) ?

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

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(\partial)/(\partial x)(ln(1+x^2+y^2))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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