Maharashtra State BoardHSC Commerce 12th Board Exam
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find dy/dx if x=e^(2t) , y=e^(√t) - Mathematics and Statistics

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Sum

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`

Concept: Derivatives of Functions in Parametric Forms
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