Differentiate the functions with respect to x
`cosx^3dotsin^2(x^5)`

Explanation

To differentiate the function \( f(x) = \cos(x^3) \cdot \sin^2(x^5) \) with respect to \( x \), we will use the product rule of differentiation. The product rule states that if you have two functions \( u \) and \( v \), then the derivative of their product is given by:

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

### Step 1: Identify \( u \) and \( v \)

...