The differentiation of `cosx` with respect to `x' is -sinxdot` i.e. `d/(dx)(cosx)=-sinx`

Explanation

To prove that the differentiation of \( \cos x \) with respect to \( x \) is \( -\sin x \), we will use the definition of the derivative based on limits.

### Step-by-Step Solution:

1. **Definition of Derivative**:
The derivative of a function \( f(x) \) is defined as:
\[
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
...