I don't really think this would count as homework help because we havn't exactly gotten to this in class. I just briefly saw it in Essential Calculus: Early Transcendentals that there are derivatives of higher orders.

Would I be correct in assuming that a derivative of the next order is just a derivative of a derivative? As in lets say that f(x) = x^4.

Using the power rule, the derivative would be:

f'(x) = 4x^3

The derivative of the next order would be:

f''(x) = 12x^2

Going along with this pattern:

f'''(x) = 24x

Would I be correct in assuming that a derivative of the next order is just a derivative of a derivative? As in lets say that f(x) = x^4.

Using the power rule, the derivative would be:

f'(x) = 4x^3

The derivative of the next order would be:

f''(x) = 12x^2

Going along with this pattern:

f'''(x) = 24x