What is (d^2)/(dx^2)((y)(e^{-3x})) ?

The answer to (d^2)/(dx^2)((y)(e^{-3x})) is 9e^{-3x}y-6e^{-3x}(dy)/(dx)+e^{-3x}(d^2y)/(dx^2)

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(d^2)/(dx^2)((y)(e^{-3x}))

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

9 e^{- 3 x} y - 6 e^{- 3 x} \frac{d y}{d x} + e^{- 3 x} \frac{d ^{2} y}{d x ^{2}}

Solution steps

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

\frac{d}{d x} (y e^{- 3 x}) = e^{- 3 x} \frac{d y}{d x} - 3 e^{- 3 x} y

= \frac{d}{d x} (e^{- 3 x} \frac{d y}{d x} - 3 e^{- 3 x} y)

\frac{d}{d x} (e^{- 3 x} \frac{d y}{d x} - 3 e^{- 3 x} y) = 9 e^{- 3 x} y - 6 e^{- 3 x} \frac{d y}{d x} + e^{- 3 x} \frac{d ^{2} y}{d x ^{2}}

= 9 e^{- 3 x} y - 6 e^{- 3 x} \frac{d y}{d x} + e^{- 3 x} \frac{d ^{2} y}{d x ^{2}}

e^{- 0.00386}

e^{- 5 t} t^{2} sin (3 t)

\frac{e ^{x}}{e ^{2}}

x^{2} - 2 x + 6 \cdot x^{2} + 2 x - 6

9^{2} - (\frac{25}{26})^{2}

What is (d^2)/(dx^2)((y)(e^{-3x})) ?
The answer to (d^2)/(dx^2)((y)(e^{-3x})) is 9e^{-3x}y-6e^{-3x}(dy)/(dx)+e^{-3x}(d^2y)/(dx^2)