Applications Of Derivatives Question 193
Question: If $ xe^{xy}=y+{{\sin }^{2}}x $ , then at $ x=0,\frac{dy}{dx}= $
[IIT 1996]
Options:
A) -1
B) -2
C) 1
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
We are given that $ xe^{xy}=y+{{\sin }^{2}}x $
When $ x=0 $ , we get $ y=0 $
Differentiating both sides with respect to x, we get
$ e^{xy}+xe^{xy}[ x\frac{dy}{dx}+y ]=\frac{dy}{dx}+2\sin x\cos x $
Putting $ x=0,,y=0 $ , we get $ \frac{dy}{dx}=1 $ .
BETA
