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Question
find dy/dx if x=e2t , y=`e^sqrtt`
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Solution
x=e2t , 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`
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