What is (d^2)/(dx^2)((y)(4(2x+2)sin(x^2+2x+pi/2))) ?

The answer to (d^2)/(dx^2)((y)(4(2x+2)sin(x^2+2x+pi/2))) is

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(d^2)/(dx^2)((y)(4(2x+2)sin(x^2+2x+pi/2)))

\frac{d ^{2}}{d x ^{2}} ((y) (4 (2 x + 2) sin (x^{2} + 2 x + \frac{π}{2})))

4 (sin (x^{2} + 2 x + \frac{π}{2}) \frac{d ^{2} y}{d x ^{2}} (2 x + 2) + 2 \frac{d y}{d x} (2 sin (x^{2} + 2 x + \frac{π}{2}) + cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{2}) + (6 cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2) - sin (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{3}) y)

Solution steps

\frac{d ^{2}}{d x ^{2}} ((y) (4 (2 x + 2) sin (x^{2} + 2 x + \frac{π}{2})))

\frac{d}{d x} (y \cdot 4 (2 x + 2) sin (x^{2} + 2 x + \frac{π}{2})) = 4 (\frac{d y}{d x} (2 x + 2) sin (x^{2} + 2 x + \frac{π}{2}) + (2 sin (x^{2} + 2 x + \frac{π}{2}) + cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{2}) y)

= \frac{d}{d x} (4 (\frac{d y}{d x} (2 x + 2) sin (x^{2} + 2 x + \frac{π}{2}) + (2 sin (x^{2} + 2 x + \frac{π}{2}) + cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{2}) y))

\frac{d}{d x} (4 (\frac{d y}{d x} (2 x + 2) sin (x^{2} + 2 x + \frac{π}{2}) + (2 sin (x^{2} + 2 x + \frac{π}{2}) + cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{2}) y)) = 4 (sin (x^{2} + 2 x + \frac{π}{2}) \frac{d ^{2} y}{d x ^{2}} (2 x + 2) + 2 \frac{d y}{d x} (2 sin (x^{2} + 2 x + \frac{π}{2}) + cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{2}) + (6 cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2) - sin (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{3}) y)

= 4 (sin (x^{2} + 2 x + \frac{π}{2}) \frac{d ^{2} y}{d x ^{2}} (2 x + 2) + 2 \frac{d y}{d x} (2 sin (x^{2} + 2 x + \frac{π}{2}) + cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{2}) + (6 cos (x^{2} + 2 x + \frac{π}{2}) (2 x + 2) - sin (x^{2} + 2 x + \frac{π}{2}) (2 x + 2)^{3}) y)

3 + 0 (x - 1)

\frac{- 2 ( 0 ) + 9}{- ( 0 ) ^{2} + 9}

dd x (e^{x^{4}} + ln (5) (π))

\frac{2}{( s + 1 ) ( s ^{2} + 4 )}

0.5 (37.622 + 16 e^{1.5 x})

What is (d^2)/(dx^2)((y)(4(2x+2)sin(x^2+2x+pi/2))) ?
The answer to (d^2)/(dx^2)((y)(4(2x+2)sin(x^2+2x+pi/2))) is