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If y=log tan.(x)/(2) , find (dy)/(dx)....

If `y=log tan.(x)/(2)` , find `(dy)/(dx)`.

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To find the derivative of the function \( y = \log \tan\left(\frac{x}{2}\right) \), we will use the chain rule and the properties of logarithms. Here’s a step-by-step solution: ### Step 1: Rewrite the function We start with the function: \[ y = \log \tan\left(\frac{x}{2}\right) \] ...
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Knowledge Check

  • If y=log[tan(pi/4 +x/2)]) ,then (dy)/(dx) is

    A
    `-tan x`
    B
    `-sec x`
    C
    tan x
    D
    sec x

  • If y= log (secx+tan x ) ,then (dy)/(dx)

    A
    ` secx `
    B
    `secx tan x `
    C
    ` tanx`
    D
    ` cos x `

  • If y= log sece^(x^(2)) ,then *(dy)/(dx)

    A
    ` xe^(x^(2)) tan e^(x^(2))`
    B
    ` 2 xe^(x^(2)) tan e^(x^(2))`
    C
    ` - xe^(x^(2)) tan e^(x^(2))`
    D
    ` - 2xe^(x^(2)) tan e^(x^(2))`

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    If y=log(sec x+tan x), then (dy)/(dx)=

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