Given that y = 4x^3 – 5/(x^2) , x =/= 0, find in its simplest form dy/dx.

We are given: y = 4x^3  – 5/(x^2) To find the dy/dx we are going to use the power rule, from the power rule differentiating x^n gives n*x^n-1, so from our equation differetiating x^3 will give 3x^2, but we need the differential of 4x^3, this will be 12x^3. The derivative of 5/(x^2) is the same as differentiating 5x^-2,  hence, again from the power rule,  differentiating 5x^-2 gives -10x^-3, which is the same as -10/(x^3) so dy/dx = 12x^2 -10/(x^3)

MA
Answered by Mohamed A. Maths tutor

5257 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Consider the closed curve between 0 <= theta < 2pi given by r(theta) = 6 + alpha sin theta, where alpha is some real constant strictly between 0 and 6. The area in this closed curve is 97pi/2. Calculate the value of alpha.


What is differentiation and how do I do it?


Differentiate the equation y = (1+x^2)^3 with respect to (w.r.t.) x using the chain rule. (Find dy/dx)


How would I go about solving 3(x-2) = x+7?


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