Question

· If x = 2t and y = 2t2, then
what is
dy ?
dx

Answer 1

$\dfrac{dy}{dx}=2t$

Step-by-step explanation:

We have,

x = 2t              ...... (1)

and,

y = 2$t^2$             ...... (2)

To find, the value of $\dfrac{dy}{dx}$ = ?

Differentiating (1) w.r.t. 't', we get

$\dfrac{dx}{dt} =2\dfrac{d(t)}{dt}$

⇒ $\dfrac{dx}{dt} =2(1)=2$   ...... (3)

Differentiating (2) w.r.t. 't', we get

$\dfrac{dy}{dt} =\dfrac{d(2t^2)}{dt}$

⇒ $\dfrac{dy}{dt} =2\dfrac{d(t^2)}{dt}$

⇒ $\dfrac{dy}{dt} =2(2t)=4t$ ...... (4)

Dividing (4) by (3), we get

$\dfrac{\dfrac{dy}{dt}}{\dfrac{dx}{dt}}=\dfrac{dy}{dx}=\dfrac{4t}{2}$

∴ $\dfrac{dy}{dx}=2t$

Hence, $\dfrac{dy}{dx}=2t$