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