Applications Of Derivatives Question 219

Question: If $ 2t=v^{2}, $ then $ \frac{dv}{dt} $ is equal to

[MP PET 1992]

Options:

A) 0

B) 1/4

C) ½

D) 1/v

Show Answer

Answer:

Correct Answer: D

Solution:

$ \Rightarrow 2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 $ ; Differentiating w.r.t. t of v, we get $ 2v\frac{dv}{dt}=2 $ or $ \frac{dv}{dt}=\frac{1}{v} $ .