\( y=\cot (5 \cdot x+3) \) Find \( \frac{d y}{d x} \) \( \frac{d y}{d x}= \)

To find the derivative \( \frac{d y}{d x} \) of the function \( y = \cot(5x + 3) \), we use the chain rule. The derivative of \( \cot(u) \) is \( -\csc^2(u) \) and we multiply by the derivative of the inner function \( u = 5x + 3 \) which is 5. So, \[ \frac{d y}{d x} = -\csc^2(5x + 3) \cdot \frac{d}{dx}(5x + 3) = -\csc^2(5x + 3) \cdot 5 \] Thus, \[ \frac{d y}{d x} = -5 \csc^2(5x + 3) \]