Differentiation Question 232
Question: $ \frac{d}{dx}\sqrt{{{\sec }^{2}}x+cose{c^{2}}x}= $
[DSSE 1981]
Options:
A) $ 4\cos \text{ec 2}x.\cot 2x $
B) $ -4\cos \text{ec 2}x.\cot 2x $
C) $ -4\cos \text{ec }x.\cot 2x $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{d}{dx}[\sqrt{{{\sec }^{2}}x+cose{c^{2}}x}]=\frac{d}{dx}[ \sqrt{( \frac{1}{{{\cos }^{2}}x}+\frac{1}{{{\sin }^{2}}x} )} ] $
$ =\frac{d}{dx}[2cosec2x]=-4cosec2x\cot 2x $ .
BETA
