Question

Find \(\frac{dy}{dx}\), if x=log⁡t^2 and y=\(\frac{1}{t}\).

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

(b) –\(\frac{t}{2}\)

(c) –\(\frac{1}{2t}\)

(d) \(\frac{t}{2}\)

I have been asked this question by my school principal while I was bunking the class.

I need to ask this question from Derivatives of Functions in Parametric Forms topic in division Continuity and Differentiability of Mathematics – Class 12

Answer 1

Right option is (c) –\(\frac{1}{2t}\)

Best explanation: Given that, x=log⁡t^2 and y=\(\frac{1}{t}\)

\(\frac{dx}{dt}\)=\(\frac{1}{t^2}.2t=\frac{2}{t}\)

\(\frac{dy}{dt}\)=-\(\frac{1}{t^2}\)

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