Problems from Derivative of the product of two functions

Find the derivative of $$f(x)=5x(5x+1)x^2$$.

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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:

$$f'(x)=15x^2(5x+1)+5x^3(5)=90x^3+15x^2$$

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