What is (d^2)/(dx^2)((y)(12x^2-12x+10)) ?

The answer to (d^2)/(dx^2)((y)(12x^2-12x+10)) is (d^2y)/(dx^2)(12x^2-12x+10)+2(dy)/(dx)(24x-12)+24y

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(d^2)/(dx^2)((y)(12x^2-12x+10))

\frac{d ^{2}}{d x ^{2}} ((y) (12 x^{2} - 12 x + 10))

\frac{d ^{2} y}{d x ^{2}} (12 x^{2} - 12 x + 10) + 2 \frac{d y}{d x} (24 x - 12) + 24 y

Solution steps

\frac{d ^{2}}{d x ^{2}} ((y) (12 x^{2} - 12 x + 10))

\frac{d}{d x} (y (12 x^{2} - 12 x + 10)) = \frac{d y}{d x} (12 x^{2} - 12 x + 10) + (24 x - 12) y

= \frac{d}{d x} (\frac{d y}{d x} (12 x^{2} - 12 x + 10) + (24 x - 12) y)

\frac{d}{d x} (\frac{d y}{d x} (12 x^{2} - 12 x + 10) + (24 x - 12) y) = \frac{d ^{2} y}{d x ^{2}} (12 x^{2} - 12 x + 10) + 2 \frac{d y}{d x} (24 x - 12) + 24 y

= \frac{d ^{2} y}{d x ^{2}} (12 x^{2} - 12 x + 10) + 2 \frac{d y}{d x} (24 x - 12) + 24 y

(1 + y^{2} + x y^{2}) d x

\frac{2659}{12 , 3} \cdot (1 + 0.17638 \cdot \frac{12 , 3}{10 , 3})

\frac{50 x}{( 20 x + 5 )}

\frac{( x - 2 ) ( x + 2 ) ( x - 3 )}{( x + 4 ) ( x ^{2} - 5 x + 12 )}

\frac{n ( n - 1 )}{n !}

What is (d^2)/(dx^2)((y)(12x^2-12x+10)) ?
The answer to (d^2)/(dx^2)((y)(12x^2-12x+10)) is (d^2y)/(dx^2)(12x^2-12x+10)+2(dy)/(dx)(24x-12)+24y