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.

Answered by Balint S. Maths tutor

6626 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve 4log₂(2)+log₂(x)=3


Evaluate the integral ∫2x√(x^2 +1) dx


A curve with equation y = f(x) passes through the point (4,25). Given that f'(x) = (3/8)*x^2 - 10x^(-1/2) + 1, find f(x).


express (3x + 5)/(x^2 + 2x - 15) - 2/(x - 3) as a single fraction its simplest form


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences