Question

If y = `"e"^x/sqrt(x)` find `("d"y)/("d"x)` when x = 1

Answer 1

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)`