The derivative of `tan45^(@)` is :

Options

A. 1
B. `cot45^(@)`
C. `-cot45^(@)`
D. 0

Answer

To find the derivative of \( \tan(45^\circ) \), we can follow these steps:

### Step 1: Understand the value of \( \tan(45^\circ) \)
We know that:
\[ \tan(45^\circ) = 1 \]

### Step 2: Recognize that \( \tan(45^\circ) \) is a constant
Since \( \tan(45^\circ) \) equals 1, it is a constant value.

### Step 3: Differentiate the constant
The derivative of a constant is always zero. Therefore, when we differentiate \( \tan(45^\circ) \) with respect to \( x \), we have:
\[ \frac{d}{dx}(\tan(45^\circ)) = \frac{d}{dx}(1) = 0 \]

### Conclusion
Thus, the derivative of \( \tan(45^\circ) \) is:
\[ 0 \]