How many times are you going to post the same question? Well, maybe it is not the same! Previously, you said "binormial", which I had first interpreted as "binomial", which you have here, but apparently you meant "bi-normal", a normal distribution in two variables. I would expect "N" to be a normal distribution which has a single variable with the mean and standard deviation as
parameters. I don't know what you mean by "N(a, b, c, d, \rho)", with 5 variables. Also, since N reduces to a function in the single variable, you should get \frac{dN}{dx}, not \frac{\partial N}{\partial x} but that is a matter of notation, not substance.
In any case, by the "chain rule", \frac{dN}{dx}= \frac{\partial N}{\partial a}\frac{da}{dx}+ \frac{\partial N}{\partial b}\frac{db}{dx}+ \frac{\partial N}{\partial c}\frac{dc}{dx}+ \frac{\partial N}{\partial d}\frac{dd}{dx}+ \frac{\partial N}{\partial \rho}\frac{d\rho}{dx}.
Since a= 0.5x+ 3, da/dx= 0.5, b= -2x, db/dx= -2, c= x^2, dc/dx= 2x, d= x+ 0.2, dd/dx= 1, \rho= 0.4x- 0.2, d\rho/dx= 0.4 so
\frac{dN}{dx}= 0.5\frac{\partial N}{\partial a}- 2\frac{\partial N}{\partial b}+ 2x\frac{\partial N}{\partial c}+ \frac{\partial N}{\partial d}+ 0.4\frac{\partial N}{\partial \rho}.