Derivative of the multiplication of two functions

The function is a product of 3 functions. Nevertheless I can rewrite it as product of two functions: $f(x)=5x^3(5x+1)$

Identifying terms: $f(x)=g(x)\cdot h(x)$

$$g(x)=5x^3 \, \ \ h(x)=5x+1$$

We calculate the derivative using the rule of the product: $$f'(x)=15x^2(5x+1)+5x^3(5)=90x^3+15x^2$$