How do I differentiate 4x^3 + 2x + x^4 with respect to x?

With differentiation and integration, we can take each term separately. In general, to difference a term involving x's with respect to x, you first multiply the power of x by the coefficient of x to find the new coefficient. You then decrease the power of x by one.

The first term in this question is 4x^3. The power of x is 3 and the coefficient of x is 4, so we multiply these together to get 12. This is the coefficient of the differential. We then decrease the original power, 3, by one. So 4x^3 differentiated is 12x^2. Similarly, 2x differentiates to become 2 (because x=x^1 and multiplying 2 and 1 gets 2, and decreasing one from this power gets 0, so we have 2x^0 and x^0=1), and x^4 differentiates to 4x^3. So the whole thing differentiated is 12x^2+2+4x^3.

LT
Answered by Laura T. Maths tutor

3329 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The points A and B have coordinates (1, 6) and (7,− 2) respectively. (a) Find the length of AB.


What is the 'chain rule'?


What is the indefinite integral ∫5exp(3-4x)dx ?


When using the addition rule in probability, why must we subtract the "intersection" to find the "union" with the Addition Rule?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning