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 sin(x)cos(x) with respect to x?
Using Discriminants to Find the Number of Roots of a Quadratic Curve
A girl kicks a ball at a horizontal speed of 15ms^1 off of a ledge 20m above the ground. What is the horizontal displacement of the ball when it hits the ground?
A block of mass M lies stationary on a rough plane inclined at an angle x to the horizontal. Find a general expression relating the coeffecient of friction between the block and the plane and the angle x. At what angle does the box begin to slide?