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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int π ((20 x)^{2} - (5 x)^{2}) d x

\int \frac{t}{t ^{4} + 49} d t

y^{^{''}} - 2 y^{^{'}} - 3 y = - 3 x e^{- x}

\int \frac{x}{x - 5} d x

x \to 0 lim (x^{3} cos (\frac{1}{x}))

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