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If y= log x . e ^((tan x + x ^(2))), " ...

If `y= log x . e ^((tan x + x ^(2))), " then" dy/(dx)` is equal to

A

`e^((tan x + x^(2)))[(1)/(x) + (sec^(2) x + x ) log x ] `

B

`e^((tan x + x^(2)))[(1)/(x) + (sec^(2) x - x ) log x ] `

C

`e^((tan x + x^(2)))[(1)/(x) + (sec^(2) x + 2x ) log x ] `

D

`e^((tan x + x^(2)))[(1)/(x) + (sec^(2) x - 2x ) log x ] `

Text Solution

Verified by Experts

The correct Answer is:
C
Given , y = log `x . e^((tan x + x^(2)))`
`therefore dy/dx = e ^((tanx + x^(2)) ). (1)/(x) x.e^((tanx + x^(2))) (sec^(2) x + 2x )`
` = e^((tan x + x^(2))[(1)/(2) + (sec^(2) x + 2x ) log x ] `
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