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

8615 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How to translate a function of form y = f(x)


Find the coordinates of the stationary point of the graph y = 3x^2 - 12x


Find the derivative of sinx, use that to find the derivative of xsinx


How do I find the co-ordinates and nature of the stationary points on a curve?


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