What is (d^2)/(dx^2)((y)(-5x^2+5x)) ?

The answer to (d^2)/(dx^2)((y)(-5x^2+5x)) is (d^2y)/(dx^2)(-5x^2+5x)+2(dy)/(dx)(-10x+5)-10y

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(d^2)/(dx^2)((y)(-5x^2+5x))

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

\frac{d ^{2} y}{d x ^{2}} (- 5 x^{2} + 5 x) + 2 \frac{d y}{d x} (- 10 x + 5) - 10 y

Solution steps

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

\frac{d}{d x} (y (- 5 x^{2} + 5 x)) = \frac{d y}{d x} (- 5 x^{2} + 5 x) + (- 10 x + 5) y

= \frac{d}{d x} (\frac{d y}{d x} (- 5 x^{2} + 5 x) + (- 10 x + 5) y)

\frac{d}{d x} (\frac{d y}{d x} (- 5 x^{2} + 5 x) + (- 10 x + 5) y) = \frac{d ^{2} y}{d x ^{2}} (- 5 x^{2} + 5 x) + 2 \frac{d y}{d x} (- 10 x + 5) - 10 y

= \frac{d ^{2} y}{d x ^{2}} (- 5 x^{2} + 5 x) + 2 \frac{d y}{d x} (- 10 x + 5) - 10 y

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What is (d^2)/(dx^2)((y)(-5x^2+5x)) ?
The answer to (d^2)/(dx^2)((y)(-5x^2+5x)) is (d^2y)/(dx^2)(-5x^2+5x)+2(dy)/(dx)(-10x+5)-10y