The parametric equations of a curve are x = e^ 3t

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The parametric equations of a curve are x=e3t,y=et,t∈R.x = e^{3t},\qquad y = e^{t},\qquad t\in\mathbb R. (i) Evaluate dydx\dfrac{dy}{dx} at t=0t = 0. (ii) Evaluate d2ydx2\dfrac{d^{2}y}{dx^{2}} at t=0t = 0.

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