Question

Find \(\frac{dy}{dx}\), if x=2e^t and y=log⁡t

(a) \(\frac{1}{2te^t}\)

(b) –\(\frac{1}{2te^t}\)

(c) \(\frac{1}{te^t}\)

(d) \(\frac{1}{e^t}\)

This question was posed to me during an online exam.

Query is from Derivatives of Functions in Parametric Forms topic in portion Continuity and Differentiability of Mathematics – Class 12

Answer 1

The correct choice is (a) \(\frac{1}{2te^t}\)

Explanation: Given that, x=2e^t and y=log⁡t

\(\frac{dx}{dt}\)=2e^t

\(\frac{dy}{dt}\)=1/t

∴\(\frac{dy}{dx}\)=\(\frac{dy}{dt}.\frac{dt}{dx}=\frac{1}{t}.\frac{1}{2e^t}=\frac{1}{2te^t}\).