Question

Find dy/dx, when x= at^2, y=2at
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Answer 1

Step-by-step explanation:

hope you got your answer

Answer 2

AnsWer :

1 / t.

SolutioN :

$\tt \dagger \: \: \: \: \: \dfrac{dy}{dx} , \: \: \: When \: \: x = at^2 , \: \: \: y = 2at.$

Case 1.

$\tt :\implies x = a {t}^{2}$

• Both sides, dx / dt ( differentiate with respect to t )

$\tt :\implies \dfrac{dx}{dt} = \dfrac{d(a {t}^{2} )}{dt}$

• Note : a constant ( taking Common )

$\tt :\implies \dfrac{dx}{dt} = a \: \dfrac{d( {t}^{2} )}{dt}$

• differentiate of t² = 2t.

$\tt :\implies \dfrac{dx}{dt} = a .\:2t$

$\tt :\implies \dfrac{dx}{dt} = 2at.$

$\rule{90}2$

Case 2.

$\tt \dagger \: \: \: \: \: y = 2at$

• Both sides, dx / dt ( differentiate with respect to t )

$\tt :\implies \dfrac{dy}{dt} = \dfrac{d(2at)}{dt}$

• Note : a , 2 are constant ( taking Common )

$\tt :\implies \dfrac{dy}{dt} = 2a \: \: \dfrac{d(t)}{dt}$

• differentiate of t = 1.

$\tt :\implies \dfrac{dy}{dt} = 2a.$

≛ According to Question.

$\tt \dagger \: \: \: \: \: \dfrac{dy}{dx}$

$\tt : \implies \dfrac{ 2a}{2at}$

$\tt : \implies \dfrac{1}{t}$

✡ Therefore, the value dy / dx = 1 / t.