if `y = tan^-1(2^x/(1+2^(2x+1)))` then `dy/dx at x =0` is

Options

A. 1
B. 2
C. In 2
D. `-(1)/(10) In 2`

Explanation

To find \( \frac{dy}{dx} \) for the function \( y = \tan^{-1}\left(\frac{2^x}{1 + 2^{2x + 1}}\right) \) at \( x = 0 \), we can follow these steps:

### Step 1: Simplify the function
We start with the function:
\[ y = \tan^{-1}\left(\frac{2^x}{1 + 2^{2x + 1}}\right) \]
We can rewrite the denominator:
...