Differentiation Question 443
Question: If $ y=\sqrt{\frac{(x-a)(x-b)}{(x-c)(x-d)}} $ , then $ \frac{dy}{dx}= $
Options:
A) $ \frac{y}{2}[ \frac{1}{x-a}+\frac{1}{x-b}-\frac{1}{x-c}-\frac{1}{x-d} ] $
B) $ y[ \frac{1}{x-a}+\frac{1}{x-b}-\frac{1}{x-c}-\frac{1}{x-d} ] $
C) $ \frac{1}{2}[ \frac{1}{x-a}+\frac{1}{x-b}-\frac{1}{x-c}-\frac{1}{x-d} ] $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=\sqrt{[ \frac{(x-a)(x-b)}{(x-c)(x-d)} ]} $
Therefore $ \log y=\frac{1}{2}[\log (x-a)+\log (x-b)-\log (x-c)-\log (x-d)] $
Differentiating w.r.t. x we get $ \frac{1}{y}\frac{dy}{dx}=\frac{1}{2}[ \frac{1}{(x-a)}+\frac{1}{(x-b)}-\frac{1}{(x-c)}-\frac{1}{(x-d)} ] $
Thus $ \frac{dy}{dx}=\frac{y}{2}[ \frac{1}{(x-a)}+\frac{1}{(x-b)}-\frac{1}{(x-c)}-\frac{1}{(x-d)} ] $ .
BETA
