Solved: "Second derivatives Find d2ydx2 for the following functions...." - Plainmath

b2sonicxh

Answered question

2021-12-08

Second derivatives Find

d^{2} \frac{y}{{d x}^{2}}

for the following functions.

y = e^{- 2 x^{2}}

Answer & Explanation

Esta Hurtado

Beginner2021-12-09Added 39 answers

Step 1
The given equation is

y = e^{- 2 x^{2}}

Differentiate with respect to x, we get

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

\frac{d y}{d x} = e^{- 2 x^{2}} \cdot (- 4 x) = - 4 x e^{- 2 x^{2}}

Step 2
Again differentiate

\frac{d^{2} y}{{d x}^{2}} = - (4 x \frac{d}{d x} (e^{- 2 x^{2}}) + e^{- 2 x^{2}} \frac{d}{d x} 4 x)

\frac{d^{2} y}{{d x}^{2}} = - (4 x (- 4 x \cdot e^{- 2 x^{2}}) + 4 e^{- 2 x^{2}})

\frac{d^{2} y}{{d x}^{2}} = 16 x^{2} e^{- 2 x^{2}} - 4 e^{- 2 x^{2}}

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