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

8677 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Do the circles with equations x^2 -2x + y^2 - 2y=7 and x^2 -10x + y^2 -8y=-37 touch and if so, in what way (tangent to each other? two point of intersection?)


A curve has equation y = f(x) and passes through the point (4,22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7 use intergration to find f(x).


Determine the coordinates of all the stationary points of the function f(x) = (1/3)*x^3+x^2-3*x+1 and state whether they are a maximum or a minimum.


Simple binomial: (1+0.5x)^4


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