Problems from Derivative of the product of two functions

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

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

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

$g (x) = 5 x^{3} h (x) = 5 x + 1$

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

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

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