Question

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

Answer 1

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

Explanation:

The derivative of a parametric function is defined by:
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`dy/dx=(dy/dt)/(dx/dt)`
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Here `x=t^2-1" "`and`" "y=te^(2t-1)`
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`dx/dt=2t`
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`dy/dt=e^(2t-1)+2te^(2t-1)=e^(2t-1)(1+2t)`
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`dy/dx=(dy/dt)/(dx/dt)=(e^(2t-1)(1+2t))/(2t)`