Question

find dy/dx if x=at⁴, y = at³
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Answer 1

Answer:

The answer for dy/dx is 3/4t .

Step-by-step explanation:

First, you have to differentiate x and y expressions in term of t :

$x = a {t}^{4}$

$\frac{dx}{dt} = 4a {t}^{3}$

$y = a {t}^{3}$

$\frac{dy}{dt} = 3a {t}^{2}$

Next, we can assume that dy/dt ÷ dx/dt = dy/dx. So we have to substitute the expressions :

$\frac{dy}{dt} \div \frac{dx}{dt} = \frac{dy}{dt} \times \frac{dt}{dx} = \frac{dy}{dx}$

$\frac{dy}{dx} = 3a {t}^{2} \div 4a {t}^{3}$

$\frac{dy}{dx} = 3a {t}^{2} \times \frac{1}{4a {t}^{3} }$

$\frac{dy}{dx} = \frac{3}{4t}$