Derivative of y=x³-5x²+7

1. Differentiate $x^{3} - 5 x^{2} + 7$ term by term:

   1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of a constant times a function is the constant times the derivative of the function.

         1. Apply the power rule: $x^{2}$ goes to $2 x$

         So, the result is: $10 x$

      So, the result is: $- 10 x$

   3. The derivative of the constant $7$ is zero.

   The result is: $3 x^{2} - 10 x$

2. Now simplify:

   $$x \left(3 x - 10\right)$$

The answer is:

$$x \left(3 x - 10\right)$$