Differentiation Question 291
Question: $ {10^{-x\tan x}}[ \frac{d}{dx}({10^{x\tan x}}) ] $ is equal to
[AMU 2000]
Options:
A) $ \tan x+x{{\sec }^{2}}x $
B) $ \ln 10(\tan x+x{{\sec }^{2}}x) $
C) $ \ln 10( \tan x+\frac{x}{{{\cos }^{2}}x}+\tan x\sec x ) $
D) $ x\tan xln10 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ {10^{-x\tan x}}\frac{d}{dx}({10^{x\tan x}}) $
= $ {10^{-x\tan x}}{{.10}^{x\tan x}}.\log 10(\tan x+x{{\sec }^{2}}x) $
= $ \log 10(\tan x+x{{\sec }^{2}}x) $ .
BETA
