If $x$ and $y$ are given parametrically in terms of $t$, then $\dfrac{dy}{dx}$ is
A$\dfrac{dx/dt}{dy/dt}$
B$\dfrac{dy/dt}{dx/dt}$
C$\dfrac{d^2y}{dt^2}$
D$\dfrac{dy}{dt}\cdot\dfrac{dx}{dt}$
Answer & Solution
Correct answer: B. $\dfrac{dy/dt}{dx/dt}$
For parametric curves, the derivative with respect to $x$ is obtained by dividing the derivative of $y$ with respect to the parameter by the derivative of $x$ with respect to the same parameter: $\dfrac{dy}{dx}=\dfrac{dy/dt}{dx/dt}$, provided $dx/dt\neq 0$.
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