What is (d^2)/(dx^2)(ln(sqrt(x^2+y^2))) ?

The answer to (d^2)/(dx^2)(ln(sqrt(x^2+y^2))) is

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(d^2)/(dx^2)(ln(sqrt(x^2+y^2)))

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

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

Solution steps

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

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

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

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

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

\int \frac{5 x ^{3}}{( x - 2 ) ( x + 3 )} d x

\frac{\partial}{\partial x} (ln (x + z) - yz)

\frac{d}{d t} (\frac{d x}{d t}) + \frac{d}{d t} (6 x) + 10 x = 0

y + 4 y^{3} = (y^{4} + 2 x) y^{^{'}}

\int x^{2} cos (k x) d x

What is (d^2)/(dx^2)(ln(sqrt(x^2+y^2))) ?
The answer to (d^2)/(dx^2)(ln(sqrt(x^2+y^2))) is