Question

find dy/dx if x=e^{2t ,} y=`e^sqrtt`

Answer 1

x=e^{2t ,} y=`e^sqrtt`

Differentiating x w.r.t t

`"dx"/"dt"=d(e^(2t))/(dt)=e^(2t)d/"dt"(2t)=2e^(2t)`

Differentiating y w.r.t t

`"dy"/"dt"=d(e^(sqrt t))/(dt)=e^(sqrt t)d/"dt"(sqrt t)=(e^(sqrt t))/(2sqrt t)`

By parametric rule we get

`dy/dx=("dy"/"dt")/("dx"/"dt")`

`=((e^(sqrt t))/(2sqrt t))/(2e^(2t))`

`=(e^sqrtt)/(4sqrt t.e^(2t))`

`e^sqrtt`