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

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

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

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

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

Solution steps

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

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

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

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

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

1.78 \cdot 1 0^{- 3}

e^{- 2 x} ln (x)

(e^{2 \cdot \frac{1}{2}})^{2}

(3 m^{2}) (2 m^{3})

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