Differentiation Question 453
Question: If $ x=at^{2},y=2at $ , then $ \frac{d^{2}y}{dx^{2}}= $
[Karnataka CET 1993]
Options:
A) $ -\frac{1}{t^{2}} $
B) $ \frac{1}{2at^{3}} $
C) $ -\frac{1}{t^{3}} $
D) $ -\frac{1}{2at^{3}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2a}{2at} $
Therefore $ \frac{dy}{dx}=\frac{1}{t}=\frac{2a}{y} $
Therefore $ y\frac{dy}{dx}=2a $
Therefore $ y\frac{d^{2}y}{dx^{2}}+{{( \frac{dy}{dx} )}^{2}}=0 $
$ \Rightarrow \frac{d^{2}y}{dx^{2}}=\frac{-{{(dy/dx)}^{2}}}{y}=-\frac{1}{2at^{3}} $ .
BETA
