Find dy/dx when x+2y+3y^2= 2x^2+1

To solve this question we can use implicit differentiation. We can write:d/dx(x+2y+3y^2)=d/dx(2x^2+1).When differentiating something in terms of y with respect to x we can use the chain rule, this allows us to differentiate with respect to y and multiply by dy/dx. 1+(d(2y)/dy)*dy/dx+(d(3y^2)/dy)*dy/dx=4x, then we differentiate our y values with respect to y: 1+2dy/dx+(6y)dy/dx=4x. Then we need to set dy/dx as the subject of the equation:dy/dx(2+6y)=4x-1, then by dividing each side by (2+6y) we get dy/dx=(4x-1)/(2+6y).

AG
Answered by Adam G. Maths tutor

3449 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A tank is filled with water up to the height H0. At the bottom of the tank, there is a tap which is opened at t=0. How does the height of liquid change with time?(Hint: dH/dt is proportional to -H)


Using integration by parts, and given f(x) = 3xcos(x), find integrate(f(x) dx) between (pi/2) and 0.


If y = 5x^3 - 2x^2 + 2, what is dy/dx?


How would you differentiate 3x^4 - 2x^2 + 9x - 1


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