If y = 5x^3 - 2x^2 + 2, what is dy/dx?

Differentiation can be done term-by-term, so we can treat the 5x³, -2x² and 2 separately. We can also 'take out' the coefficients: to differentiate 5x³, for example, differentiate x³ first and then multiply by 5.

For the first term: x³ differentiates to 3x², so we get 15x².

Second term: x² differentiates to 2x, so we have -4x.

Third term: The derivative of a constant is zero.

The answer is just the sum of these, which is 15x² - 4x.