Question 375858
Use implicit differentiation, treat each terms as if it is differentiable (other than constants). Use the product rule, etc. to simplify. Gather up all of the dy and dx terms and then form the quotient, dy/dx.
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I'll do one, you do the rest.
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{{{y - x*sin(y) - 3x^2 - 1=0}}}
{{{dy-(x*cos(y)dy+sin(y)*dx)-6xdx=0}}}
{{{dy-x*cos(y)dy=6xdx+sin(y)dx}}}
{{{dy(1-x*cos(y))=(6x+sin(y))dx}}}
{{{highlight(dy/dx=(6x+sin(y))/(1-x*cos(y)))}}}