Differentiation Question 379
Question: If $ x=a\sin \theta $ and $ y=b $
$ \cos \theta , $ then $ \frac{d^{2}y}{dx^{2}} $ is
[UPSEAT 2002]
Options:
A) $ \frac{a}{b^{2}}{{\sec }^{2}}\theta $
B) $ \frac{-b}{a}{{\sec }^{2}}\theta $
C) $ \frac{-b}{a^{2}}{{\sec }^{3}}\theta $
D) $ \frac{-b}{a^{2}}{{\sec }^{3}}\theta $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dx}{d\theta }=a\cos \theta $ and $ \frac{dy}{d\theta }=-b\sin \theta $
Therefore $ \frac{dy}{dx}=\frac{-b}{a}\tan \theta $ and $ \frac{d^{2}y}{dx^{2}}=\frac{-b}{a}{{\sec }^{2}}\theta \frac{d\theta }{dx} $
Therefore $ \frac{d^{2}y}{dx^{2}}=\frac{-b}{a}{{\sec }^{2}}\theta \frac{1}{a\cos \theta }=\frac{-b}{a^{2}}{{\sec }^{3}}\theta $ .
BETA
