Question

If \(x=3at^2\), \(y=3at^4\) then \(\frac{dy}{dx}\) is:

• A. 3at
• B. 12at³
• C. 6at
• D. 2t²

Answer 1

The Correct Option is D

To find \(\frac{dy}{dx}\) where \(x=3at^2\) and \(y=3at^4\), we use implicit differentiation. Start by differentiating each variable with respect to the parameter \(t\):
Step 1: Differentiate \(x\) with respect to \(t\):
\(\frac{dx}{dt}=6at\)
Step 2: Differentiate \(y\) with respect to \(t\):
\(\frac{dy}{dt}=12at^3\)
Step 3: Use the chain rule to find \(\frac{dy}{dx}\):
\(\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{12at^3}{6at}\)
Step 4: Simplify the expression:
\(\frac{dy}{dx} = 2t^2\)
Thus, the answer is \(2t^2\).