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.
