Find an equation of the tangent line to the curve 2(x^2+y^2)2=25(x^2−y^2) (a lemniscate) at the point (3,1)

notice... a derivative is just the function for the slope

now, you're given the point 3,1, namely x = 3 and y = 1

to find the "m" or slope, use that derivative, namely 

that'd give you a value for the slope

to get the tangent line at that point, simply plug in the provided values
in the point-slope form



and then you solve it for "y", I gather you don't have to, but that'd be the equation of the tangent line at 3,1

The correct answer would be shape of function b = 2× slope of function a.