What is the derivative of f(t) = (t^2-1 , te^(2t-1) ) f(t)=(t21,te2t1)?

1 Answer
Apr 24, 2017

dy/dx=(e^(2t-1)(1+2t))/(2t)dydx=e2t1(1+2t)2t

Explanation:

The derivative of a parametric function is defined by:
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dy/dx=(dy/dt)/(dx/dt)dydx=dydtdxdt
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Here x=t^2-1" "x=t21 and" "y=te^(2t-1) y=te2t1
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dx/dt=2tdxdt=2t
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dy/dt=e^(2t-1)+2te^(2t-1)=e^(2t-1)(1+2t)dydt=e2t1+2te2t1=e2t1(1+2t)
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dy/dx=(dy/dt)/(dx/dt)=(e^(2t-1)(1+2t))/(2t)dydx=dydtdxdt=e2t1(1+2t)2t