1. The problem statement, all variables and given/known data Find dy/dx on the curve 1/3*y^3 + y*sin(x) = 1 - x^6 At which points on the curve does this derivative does not exist? Find the slope of the line tangent to the curve at the point (0,3^(1/3)). 2. Relevant equations dy/dx = - Fx/Fy 3. The attempt at a solution I solved dy/dx implicitly using the above formula to get: dy/dx = - (y*cos(x) + 6x^5) / (y^2 + sin(x)) To find the points where dy/dx doesn't exist, I let: y^2 + sin(x) = 0 I've then tried rearranging the above expression in terms of y and x and substituing into the original curve equation, but can't complete the algebra by hand. Wolfram returned multiple answers depending how it's done. Any help? Thank you! :) EDIT: And for the last bit, I would just substitute those values for x and y into dy/dx which gives me something about -0.6 from memory?