Differentiation Question 422
Question: If $ x=a{{\cos }^{4}}\theta ,y=a{{\sin }^{4}}\theta , $ then $ \frac{dy}{dx} $ , at $ \theta =\frac{3\pi }{4} $ , is
[Kerala (Engg.) 2002]
Options:
A) -1
B) 1
C) $ -a^{2} $
D) $ a^{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=a{{\sin }^{4}}\theta $
Therefore $ \frac{dy}{d\theta }=4a{{\sin }^{3}}\theta \cos \theta $
and $ x=a{{\cos }^{4}}\theta $
Therefore $ \frac{dx}{d\theta }=-4a{{\cos }^{3}}\theta \sin \theta $
\ $ \frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }=\frac{-{{\sin }^{2}}\theta }{{{\cos }^{2}}\theta }=-{{\tan }^{2}}\theta $
\ $ {{( \frac{dy}{dx} )} _{\theta =\frac{3\pi }{4}}}=-{{\tan }^{2}}( \frac{3\pi }{4} )=-1 $ .
BETA
