The curve C has equation ye^(-2x) = 2x + y^2. Find dy/dx in terms of x and y.

The curve's equation is presented as an implicit function. Therefore we must use implicit differentiation to solve this problem. To do this, we differentiate both sides of the equation with respect to x, applying the chain rule where a y variable appears, and then rearrange to give dy/dx. The equation given in the question differentiates implicitly to e-2x(dy/dx) - 2ye-2x = 2 + 2y(dy/dx). This can be rearranged to dy/dx = (2 + 2ye-2x )/ (e-2x- 2y)

GW
Answered by Georgia W. Maths tutor

8446 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Write down three linear factors of f(x) such that the curve of f(x) crosses the x axis at x=0.5,3,4. Hence find the equation of the curve in the form y = 2(x^3) + a(x^2) + bx + c.


Implicitly differentiate the following equation to find dy/dx in terms of x and y: 2x^2y + 2x + 4y – cos (piy) = 17


When trying to solve inequalities (e.g. 1/(x+2)>x/(x-3)) I keep getting the wrong solutions even though my algebra is correct.


How can I improve my mathematics


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