Find the derivative of the function y = x (x²-4)

To complete this task, we apply the rules for finding the derivative, and since the original expression is a product, the derivative of this expression is equal to the sum of the products of the derivative of the first factor by the second plus the first factor multiplied by the derivative of the second factor;

y ‘= (x (x ^ 2 – 4))’ = x ‘(x ^ 2 – 4) + x (x ^ 2 – 4))’, we use the table of derivatives of elementary functions:

x ‘= 1;

x ^ 2) ‘= 2 x;

(4) ‘= 0;

(x ^ 2 – 4) ‘= (x ^ 2)’ + (-4) ‘= 2 x, the derivative of the sum is equal to the sum of the derivatives of each term;

Substitute it into the original expression and get the answer:

y ‘= 1 * (x ^ 2 – 4) + x * 2x = 3x ^ 2 – 4.