Math, asked by adit4277, 11 months ago

if x=t^2-1 and y=2e^t then find dy/dx​

Answers

Answered by rishu6845
4

Answer:

dy / dx = eᵗ t⁻²

Step-by-step explanation:

Given---> x = t² - 1 , y = 2eᵗ

To find ---> dy / dx

Solution---> We have some formulee from diferentiation , as follows,

(1) d/dx (xⁿ) = n xⁿ⁻¹

(2) d/dx ( eˣ ) = eˣ

ATQ,

x = t² - 1

Differentiatong with respect to t we get

dx / dt = d / dt ( t² - 1 )

= 2t - 0

= 2t

y = 2eᵗ

Differentiating with respect to t we get

dy / dt = 2 d / dt ( eᵗ )

= 2 eᵗ

Now, dy/ dx = ( dy / dt ) / ( dx / dt )

= 2eᵗ / 2t²

Cancel out 2 from numerator and denominator , we get

dy / dx = eᵗ t⁻²

Answered by StyloBabiie
1

Answer:

Step-by-step explanation:

Given---> x = t² - 1 , y = 2eᵗ

To find ---> dy / dx

Solution---> We have some formulee from diferentiation , as follows,

(1) d/dx (xⁿ) = n xⁿ⁻¹

(2) d/dx ( eˣ ) = eˣ

ATQ,

x = t² - 1

Differentiatong with respect to t we get

dx / dt = d / dt ( t² - 1 )

= 2t - 0

= 2t

y = 2eᵗ

Differentiating with respect to t we get

dy / dt = 2 d / dt ( eᵗ )

= 2 eᵗ

Now, dy/ dx = ( dy / dt ) / ( dx / dt )

= 2eᵗ / 2t²

Cancel out 2 from numerator and denominator , we get

dy / dx = eᵗ t⁻²

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