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Question
Differentiate the following:
y = `x"e"^(-x^2)`
Solution
y = `x"e"^(-x^2)`
y = uv where u = x and v = `"e"^(-x^2)`
Now u’ = 1 and v’ = `"e"^(-x^2) (- 2x)`
v’ = `- 2x"e"^(-x^2)`
Now y = uv
⇒ y’ = uv’ + vu’
(i..e.) `("d"y)/("d"x) = x[- 2x"e"^(-x^2)] + "e"^(-x^2) (1)`
= `"e"^(- x^2) (1 - 2x^2)`
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