If \( x=2at^{5} \) and \( y=at^{10} \), then \( \displaystyle\frac{dy}{dx}= \)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( t^{5} \)
For parametric equations, \( \frac{dy}{dx}=\frac{dy/dt}{dx/dt} \):
\( \displaystyle \frac{dx}{dt}=10at^{4},\qquad \frac{dy}{dt}=10at^{9} \)
\( \displaystyle \frac{dy}{dx}=\frac{10at^{9}}{10at^{4}} \)
\( \displaystyle =t^{5} \)