`(3x+5)(1+tanx)`

Explanation

To differentiate the function \( y = (3x + 5)(1 + \tan x) \) with respect to \( x \), we will use the product rule of differentiation. The product rule states that if you have two functions \( u(x) \) and \( v(x) \), then the derivative of their product is given by:

\[ \frac{d}{dx}[u(x)v(x)] = u(x) \frac{dv}{dx} + v(x) \frac{du}{dx} \]

### Step-by-step Solution:

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