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 ▸Find the exact solution, in its simplest form, to the equation ln(4y + 7) = 3 + ln(2 – y) (Core Maths 3 Style Question)
Find the roots of y=x^{2}+2x+2
The equation of a circle is x^2-6x+y^2+4y=12. Complete the square to find the centre and radius of the circle.
How to find out where 2 lines cross/simultaneous equations