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).

Answered by Adam G. Maths tutor

3190 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The region R is bounded by the curve y=sqrt(x)+5/sqrt(x) the x-axis and the lines x = 3, x = 4. Find the volume generated when R is rotated through four right-angles about the x-axis. Give your answer correct to the nearest integer.


Differentiate y=x*ln(x^3-5)


The line AB has equation 5x + 3y + 3 = 0 . (a) The line AB is parallel to the line with equation y = mx + 7 . Find the value of m. [2 marks] (b) The line AB intersects the line with equation 3x -2y + 17 = 0 at the point B. Find the coordinates of B.


Express x^2-7x+2 in the form (x-p)^2+q where p and q are rational. Hence or otherwise find the minimum value of x^2-7x+2


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