What is (d^2)/(dx^2)((y)(3x^2+5e^x)) ?

The answer to (d^2)/(dx^2)((y)(3x^2+5e^x)) is (d^2y)/(dx^2)(3x^2+5e^x)+2(dy)/(dx)(6x+5e^x)+(6+5e^x)y

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(d^2)/(dx^2)((y)(3x^2+5e^x))

\frac{d ^{2}}{d x ^{2}} ((y) (3 x^{2} + 5 e^{x}))

\frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y

Solution steps

\frac{d ^{2}}{d x ^{2}} ((y) (3 x^{2} + 5 e^{x}))

\frac{d}{d x} (y (3 x^{2} + 5 e^{x})) = \frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y

= \frac{d}{d x} (\frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y)

\frac{d}{d x} (\frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y) = \frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y

= \frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y

lo g_{9} (\frac{z ^{5}}{x m ^{5}})

3 (n (n + 1))

\frac{( w + 4 ) ( y )}{2}

sin (x) (4 (cos (2 x))^{2} + 2 cos (x) - 1)

\frac{d}{d t} ((x) (3 x + 2 y + 4 z))

What is (d^2)/(dx^2)((y)(3x^2+5e^x)) ?
The answer to (d^2)/(dx^2)((y)(3x^2+5e^x)) is (d^2y)/(dx^2)(3x^2+5e^x)+2(dy)/(dx)(6x+5e^x)+(6+5e^x)y