What is (d^2)/(dx^2)((y)x(x-2)) ?

The answer to (d^2)/(dx^2)((y)x(x-2)) is x(d^2y)/(dx^2)(x-2)+2(dy)/(dx)(2x-2)+2y

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(d^2)/(dx^2)((y)x(x-2))

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

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

Solution steps

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

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

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

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

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

\frac{s + 1}{s ( s ^{2} + 2 s + 2 )}

\frac{( x - 6 ) ( x + 1 )}{( x - 3 ) ( x + 2 )}

(x^{2} (1 + x))!

\frac{( 4 s ^{2} - 1 ) ^{2}}{s ^{6}}

- \frac{( x + 1 ) ( x - 4 )}{6}

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