x & y are related by kx^2(y)=c, where k and c are constants. if there is a 3% chng in y, find approx chng of x

Question

Two variables x and y are related by the equation kx^2(y)=c, where k and c are constants. If there is a 3% change in value of y, find approximate change of x using calculus.

Answer 1

Let´s find the derivative .As x^2y = e^2ylnx
k* e^2ylnx =c Taking the derivaltive of both sides

2k*e^ylnx*(y/x+y´lnx)=0 so y/x+y´lnx mus be 0 and¨

y´= -y /(xlnx).For very small changes of y you usually approximate

dy/dx with Dy/Dx ( D means delta)

if Dy is 0,03 0,03/Dx = -y/xlnx and Dx = -0.03y/xlnx where x and y are the original values (before the 3% change)