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Question
If y = `"e"^x/sqrt(x)` find `("d"y)/("d"x)` when x = 1
Solution
y = `"e"^x/sqrt(x)`
Differentiating w.r.t.x we get.
`("d"y)/("d"x) = "d"/("d"x) ("e"^x/sqrt(x))`
`("d"y)/("d"x) = (sqrt(x)"d"/("d"x) "e"^x - "e"^x "d"/("d"x) sqrt(x))/(sqrt(x))^2`
= `(sqrt(x) "e"^x - "e"^x 1/(2sqrt(x)))/x`
`("d"y)/("d"x) = (2x * "e"^x - "e"^x)/(2sqrt(x)*x)`
`("d"y)/("d"x)` at x = 1
`("d"y)/("d"x) = (2(1)"e"^1 - "e"^1)/(2sqrt(1)*1)`
= `(2"e" - "e")/2`
= `"e"/(2)`
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