Question

if x=atpower4,y=bt³then find dy/dx​

Answer 1

⇒Answer :

dy/dx = 3b / 4at

⇒Given :

x = $at^{4}$

y = bt³

⇒To Find  :

dy/dx

⇒Solution :

x =$at^{4}$

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

⇒  $\frac{dx}{dt} = 4at^{3}$   ___(1)

y = bt³

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

⇒   $\frac{dy}{dt} = 3bt^{2}$

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

$\frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{dy}{dt} * \frac{dt}{dx}$    

$\frac{dy}{dx}$ =   $3bt^{2}$ × $\frac{1}{4at^{3} }$

$\frac{dy}{dx}$ = 3b / 4at

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