how to finding a partial differential for binormial distribution?

N, as you show it, is a function of 5 variables. If we call them "p, q, r, s, and t" then we can write this as \(\displaystyle \frac{d N(p, q, r, s, t)}{d x}\) (strictly speaking, since N reduces to a function of the single variable, x, this should be "\(\displaystyle \frac{dN}{dx}\)" not "\(\displaystyle \frac{\partial N}{\partial x}\)", an ordinary derivative, not a partial derivative). By the "chain rule" \(\displaystyle \frac{d N(p, q, r, s, t)}{d x}=\)\(\displaystyle \frac{\partial N}{\partial p}\frac{dp}{dx}+ \)\(\displaystyle \frac{\partial N}{\partial q}\frac{dq}{dx}\)\(\displaystyle + \)\(\displaystyle \frac{\partial N}{\partial r}\frac{dr}{dx}+ \frac{\partial N}{\partial s}\frac{ds}{dx}+ \frac{\partial N}{\partial t}\frac{dt}{dx}\). Since we are given that p= 0.5x+ 3, q= -2x, \(\displaystyle r= x^2\), s= x+ 0.2, and t= 4x- 0.2, that can be written \(\displaystyle \frac{dN(0.5x+ 3, -2x, x^2, x+ 0.2, 4x- 0.2)}{dx}= \frac{\partial N}{\partial p}(0.5)+ \frac{\partial N}{\partial q}(-2)+ \frac{\partial N}{\partial r}(2x)+ \frac{\partial N}{\partial s}(1)+ \frac{\partial N}{\partial t}(4)\).

Now, the question is, what are all those partial derivatives? You say N is the binomial distribution. What are those variables, that I have called p, q, r, s, and t, and how does the binomial distribution depend upon each?
 
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Thanks very much.
more specifically, I want to know how to deal with the corrlation function, as following question.
could you tell me how to deal with this issues. Thanks.
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