Question

if x=at²,y=2at then dy/dx=​

Answer 1

EXPLANATION.

⇒ x = at²  and  y = 2at.

As we know that,

⇒ x = at².

Differentiate both sides w.r.t (t), we get.

⇒ dx/dt = 2at.

⇒ y = 2at.

Differentiate both sides w.r.t (t), we get.

⇒ dy/dt = 2a.

We can write equation as,

⇒ dy/dx = [dy/dt]/[dx/dt].

⇒ dy/dx = (2a)/(2at).

⇒ dy/dx = 1/t.

                                                                                                                 

MORE INFORMATION.

(1) d(sin x)/dx = cos x.

(2) d(cos x)/dx = - sin x.

(3) d(tan x)/dx = sec²x.

(4) d(cosec x)/dx = - cosec x cot x.

(5) d(sec x)/dx = sec x tan x.

(6) d(cot x)/dx = - cosec²x.

Answer 2

Answer:

Required Answer:-

Accórding to the Question ,

$\sf{x = at {}^{2} ,y = 2at }$

$\sf \red{x = {at}^{2}...(i) }$

Dif both side,

$\sf{ \frac{dx}{dt} = a \frac{d(t) {}^{2} }{dt} }$

$\sf{ \frac{dx}{dt} = a.2t }$

$\sf{ \frac{dx}{dt} = 2at }$

$\sf \red{y = 2at..(ii)}$

Dif. both sides ,

$\sf{ \frac{dy}{dt} = 2a \frac{d(t)}{dt} }$

$\sf{ \frac{dy}{dt} = 2a.1 }$

$\sf{ \frac{dy}{dt} = 2a }$

$\sf \pink{ \frac{dy}{dt} = \frac{2a}{2at} }$

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