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Find the derivative of
a) y=cos (x/2)
b) yx-3x^2 +6 = y^4 + x

a) -sin (x/2)(2+x)/2^2
b) x dy/dx + y - 6x = 4y^3 dy/dx + 3x^2
dy/dx (x -4 y^3) = 3x^2 -y +6x
dy/dx = (3x^2 -y +6x)/(x -4 y^3)
I used inplicit differation for part b

are these correct? Thanks for your help in advance!

your first answer makes no sense.
you are simply finding the derivative of
y = cos (1/2)x
which is
y'=-1/2 sin (x/2)

your second equation:
If your last term of the equation was a typo and it was x^3, then you are correct.
I like the way you showed the first line of your implicit derivative, but according to that line the last term must have been x^3 instead of x.

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