Did I implicitly differentiate correctly

Differentiate implicitly to find dp/dx

p^2 + p + 2x = 40
d/dx(p^2 + p + 2x) = d/dx(40)
2p(dp/dx) + (dp/dx) + 2*1 = 0
(2p + 1)(dy/dx) = -2
dp/dx = -2 / 2p + 1

Did I implicitly differentiate correctly? If not, how does this problem work? Please show the steps! Thanks :)

I do it one term at a time:

D(p^2 + p + 2x) = D(40)
D(p^2) + D(p) + D(2x) = 0
2p dp + dp + 2 dx = 0
(2p+1) dp = -2 dx
dp/dx = -2 / (2p+1)

I find it easier that way

Doing it directly as a d/dx of "something" can get confusing when you have terms with both variables in it (this problem does not, but later, you will get them)

YES , but use brackets dp/dx = -2 /( 2p + 1)