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

The answer to (d^2)/(dx^2)((y)(-2x^2+5x)) is (d^2y)/(dx^2)(-2x^2+5x)+2(-4x+5)(dy)/(dx)-4y

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

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

\frac{d ^{2} y}{d x ^{2}} (- 2 x^{2} + 5 x) + 2 (- 4 x + 5) \frac{d y}{d x} - 4 y

Solution steps

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

\frac{d}{d x} (y (- 2 x^{2} + 5 x)) = \frac{d y}{d x} (- 2 x^{2} + 5 x) + (- 4 x + 5) y

= \frac{d}{d x} (\frac{d y}{d x} (- 2 x^{2} + 5 x) + (- 4 x + 5) y)

\frac{d}{d x} (\frac{d y}{d x} (- 2 x^{2} + 5 x) + (- 4 x + 5) y) = \frac{d ^{2} y}{d x ^{2}} (- 2 x^{2} + 5 x) + 2 (- 4 x + 5) \frac{d y}{d x} - 4 y

= \frac{d ^{2} y}{d x ^{2}} (- 2 x^{2} + 5 x) + 2 (- 4 x + 5) \frac{d y}{d x} - 4 y

- \frac{14}{( x - 7 ) ^{2}}

h (\frac{3 x + 5}{x + 1} + 2)

\frac{4 ( 8 + x )}{( x + 4 ) ^{2} ( x - 4 )}

\frac{( x + 1 )}{( x - 0.5 ) ^{2}}

\frac{x ^{8} + y ^{3}}{( x + y ) ^{3}}

What is (d^2)/(dx^2)((y)(-2x^2+5x)) ?
The answer to (d^2)/(dx^2)((y)(-2x^2+5x)) is (d^2y)/(dx^2)(-2x^2+5x)+2(-4x+5)(dy)/(dx)-4y