Differentiation Question 423
Question: If $ x={{\sin }^{-1}}(3t-4t^{3}) $ and $ y={{\cos }^{-1}}\sqrt{(1-t^{2})} $ , then $ \frac{dy}{dx} $ is equal to
[Kerala (Engg.) 2002]
Options:
A) ½
B) 2/5
C) 3/2
D) 1/3
Show Answer
Answer:
Correct Answer: D
Solution:
$ y={{\cos }^{-1}}\sqrt{1-t^{2}}={{\sin }^{-1}}t $
and $ \frac{du}{ds}=2x.\frac{dx}{ds}+2y.\frac{dy}{ds} $
$ \frac{d^{2}y}{ds^{2}}=0 $
Therefore $ y=2s-t $ .
BETA
