Given that y =2x^3 + 3/(x^2), find a) dy/dx and b) the integral of y

a) It is useful to rewrite the equation using power rules, so we get y = 2x3 + 3x-2Now we can simply use the differentiation rules where we multiply the coefficient (number before x) by the power, then reducing the power by one.This way we get dy/dx = 6x2 - 6x-3b) Once again it is simpler to integrate y = 2x3 + 3x-2We use the integration rules of increasing the power by one then dividing the coefficient by the new power:(2x4)/4 + (3x-1)/1 + c= (x4)/2 - 3x-1 + cRemember, as we are doing indefinite integration (integrating y but not between 2 limits), we must add a constant that we can call c.

BS
Answered by Balint S. Maths tutor

7009 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you differentiate the curve y = 4x^2 + 7x + 1? And how do you find the gradient of this curve?


How do you find the turning points of a curve described by the equation y(x)?


Differentiate y=(4x^2-1)^3


f(x) = (sin(x))^3. What is f'(x)


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences