Consider the given function.
y=e√2x+1
On differentiating both sides w.r.t x, we get
y=e√2x+1
dydx=e√2x+1×(12√2x+1×2)
dydx=(e√2x+1√2x+1)
On putting x=12, we get
dydx∣∣∣x=12=(e√24+1√24+1)
dydx∣∣∣x=12=(e√25√25)
dydx∣∣∣x=12=e55
Hence, this is the answer.