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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (ln (y - 3 x))

\int - 24 t e^{- 3 t} d t

\int \frac{x ^{2} - x + 2}{x ^{4} + 4 x ^{2} + 3} d x

\int i n^{2} x d x

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