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

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

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

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

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

Solution steps

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

Treat

a, y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

Simplify

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

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

x \to 2 lim (2 x^{3} - 3 x^{2} + 4 x - 9)

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

x \to 0 lim (\frac{3}{x ( x + 3 ) ^{2}})

\int_{1}^{e} x ln (x) d x

\frac{d ^{2} y}{d x ^{2}} - y = 0

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