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 ▸Integrate x^2e^x with respect to x between the limits of x=5 and x=0.
A particle of mass 0.5 kg is moving down a rough slope (with coefficient of friction = 0.2) inclined at 30 degrees to the horizontal. Find the acceleration of the particle. Use g = 9.8 ms^-2.
How would I differentiate a function such as f(x)=x^3(e^(2x))?
Find all solutions to the trig equation 2sin(x)^2 + 3sin(x) - 2 = 0 in the range 0 <= x <= 360 degrees