Question

Find dy/dx if x=2e^-t y=4e^t

Answer 1

Step-by-step explanation:

so the answer is -2e^t/e^-t

Answer 2

Answer:

The solution is  $\frac{dy}{dx}$ =  $-2e^{2t}$

Step-by-step explanation:

x = 2$e^{-t}$ and y = 4$e^{t}$

We have to find the value of $\frac{dy}{dx}$

We know that (x)ᵃ(x)ᵇ = (x)ᵃ⁺ᵇ

Derivative of $e^{-t} = -e^{t}$ and

Derivative of $e^{t} =e^{t}$

x = 2$e^{-t}$

Differentiate with respect to 't'

$\frac{dx}{dt} =2 \frac{d}{dt} (e^{-t} )$

      = $2(-e^{-t} )$ ------------(1)

y = 4$e^{t}$

Differentiate with respect to 't'

$\frac{dy}{dt } =4\frac{d}{dt}(e^{t} ) = 4e^{t}$ --------------(2)

equation(2) divided by equation(1)

$\frac{\frac{dy}{dt} }{\frac{dx}{dt} } = \frac{4e^{t} }{2(-e^{-t}) }$

$\frac{dy}{dx} = -2e^{t} e^{t}$

    = $-2e^{2t}$

Therefore, $\frac{dy}{dx}$ =  $-2e^{2t}$