The question is:
Find slopes of all lines tangent to the graph of the relation:
y^3 + 15x^15y^2 - 50y = 150 - 150x^5
at the points on its graph where x=1
as a genral solution you can sovle all problems like yours with this approach:
first sort it as:
then use this formula to differntiate:
it means when you are differntiatig a respect to x then y assumed as constant and in reverse; be sure before differniation that all statements of the equation should be sored on one side and other side should be only Zero(0).