Question

If
$x = a {t}^{2} \\ and \\ y = 2at \\ \\ find \\ \frac{dy}{dx}$
​

Answer 1

Answer:

1/t

Step-by-step explanation:

x = at² and y = 2at.

Differentiating with respect to 't', we get

=> dx/dt = 2at and dy/dt = 2a

By the chain rule, we have

dy/dx

=> [(dy/dt)]/[(dx/dt)]

=> 2a/2at

=> 1/t

Hence, the value of dy/dx = 1/t.

#Hope my answer help you!

Answer 2

$\huge \red{\mathfrak{solution}}$

Given :

x=at^2 and y = 2at

To find : dy/dx

◆ First differentiate (x)w.r.t (t )

$\leadsto \: \frac{d}{dt} (a {t}^{2}) = 2at$

◆ Now differentiate (y) w.r.t (t)

$\leadsto \: \frac{d}{dt} (2at) = 2a$

Now: dy/dx

$\leadsto \: \frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} } \\ \\ \leadsto \: \frac{dy}{dx} = \frac{2a}{2at} \\ \\ \leadsto \: \frac{dy}{dx} = \cancel \frac{2a}{2a} \frac{1}{t} \\ \\ \leadsto \: \frac{dy}{dx} = \frac{1}{t}$

Hence the value is

$\huge\boxed{ \green{ \bold{\frac{1}{t} }} }$