Find the derivative of $$f(x)=5x(5x+1)x^2$$.
See development and solution
Development:
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: $$$f'(x)=15x^2(5x+1)+5x^3(5)=90x^3+15x^2$$$
Solution:
$$f'(x)=15x^2(5x+1)+5x^3(5)=90x^3+15x^2$$