1.

If x=at² and y=bt³ then dy/dx is

Answer»

Answer

  • dy/dx = 3bt/2a

Given

  • x = at²
  • y = bt³

To Find

  • dy/dx

Solution

  • x = at²

Differentiating the equation with respect to t on both SIDES , we get ,

\implies \rm \dfrac{d}{dt}(x)=\dfrac{d}{dt}(at^2)\\\\\implies \rm \dfrac{dx}{dt}=a\dfrac{d}{dt}(t^2)\\\\\implies \rm \dfrac{dx}{dt}=a(2t)\\\\\implies \rm \dfrac{dx}{dt}=2at...(<klux>1</klux>)

  • y = bt³

Differentiate the equation with respect to t on both sides , we get ,

\implies \rm \dfrac{d}{dt}(y)=\dfrac{d}{dt}(bt^3)\\\\\implies \rm \dfrac{dy}{dt}=b\dfrac{d}{dt}(t^3)\\\\\implies \rm \dfrac{dy}{dt}=b(3t^2)\\\\\implies \rm \dfrac{dy}{dt}=3bt^2...(2)

Now , SOLVE (2) / (1) , we get ,

\implies \rm \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}=\dfrac{3bt^2}{2at}\\\\\implies \rm \dfrac{dy}{dt}\times \dfrac{dt}{dx}=\dfrac{3bt}{2a}\\\\\implies \rm \dfrac{dy}{dx}=\dfrac{3bt}{2a}


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