The curve C has the equation ye ^(–2x) = 2x + y^2 . Find dy/dx in terms of x and y.
differentiate both side with respect to x : (dy/dx)e^(-2x)+y(-2e^(-2x)) = 2+2y(dy/dx)
rearrange it : (-2y+e^(-2x))(dy/dy) = 2 + 2ye^(-2x) ==> dy/dx = ( 2 + 2ye^(-2x) ) / ( -2y+e^(-2x) )
JC
Related Maths A Level answers
All answers ▸differentiate the following to find the equation for the gradient of the curve in terms of x and y: 3x^3 + 4x^2 + 5xy + 7y = 0
The curve C has the equation: y=3x^2*(x+2)^6 Find dy/dx
Using the identity cos(A+B)= cosAcosB-sinAsinB, prove that cos2A=1-2sin^2A.
How to integrate by parts