What is (\partial)/(\partial x)(ln(x^2+y^2+3)) ?

The answer to (\partial)/(\partial x)(ln(x^2+y^2+3)) is (2x)/(x^2+y^2+3)

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(\partial)/(\partial x)(ln(x^2+y^2+3))

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

\frac{2 x}{x ^{2} + y ^{2} + 3}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{2} + y ^{2} + 3} \frac{\partial}{\partial x} (x^{2} + y^{2} + 3)

= \frac{1}{x ^{2} + y ^{2} + 3} \frac{\partial}{\partial x} (x^{2} + y^{2} + 3)

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

= \frac{1}{x ^{2} + y ^{2} + 3} \cdot 2 x

Simplify

\frac{1}{x ^{2} + y ^{2} + 3} \cdot 2 x : \frac{2 x}{x ^{2} + y ^{2} + 3}

= \frac{2 x}{x ^{2} + y ^{2} + 3}

What is (\partial)/(\partial x)(ln(x^2+y^2+3)) ?
The answer to (\partial)/(\partial x)(ln(x^2+y^2+3)) is (2x)/(x^2+y^2+3)