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

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

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

\frac{\partial}{\partial x} (lo g_{e} (x^{2} + y^{2}))

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

Solution steps

\frac{\partial}{\partial x} (lo g_{e} (x^{2} + y^{2}))

Simplify

lo g_{e} (x^{2} + y^{2}) : ln (x^{2} + y^{2})

= \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}) = 2 x

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

Simplify

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

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

\int \frac{( 5 t - t )}{3 t ^{2} - 9} d t

\frac{\partial}{\partial x} (x^{4} - 3 x^{2} y^{2} + y^{4})

x \to - 2 lim (4^{2} - 3)

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

f (x) = 4 x^{2} - 1

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