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Question
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
Options
`(2x"e"^(x/(1 + x)))/(1 + x)^2`
`(-2x"e"^(x/(1 + x)))/(1 + x)^2`
`("e"^(x/(1 + x)))/(1 + x)^2`
`(-"e"^(x/(1 + x)))/(1 + x)^2`
MCQ
Fill in the Blanks
Solution
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = `("e"^(x/(1 + x)))/(1 + x)^2`.
Explanation:
y = `x/"e"^(1 + x)`
∴ `("d"y)/("d"x) = "e"^(x/(1 + x)) * "d"/("d"x) (x/(1 + x))`
= `"e"^(x/(1 + x))*[((1 + x)*(1) -x*(0 + 1))/(1 + x)^2]`
= `"e"^(x/(1 + x))/(1 + x)^2`
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