Could somebody help me 'total differentiate' this question please?
K = 12x^3y + 10x^2y^2 + 6xy^3 +4y^4
I don't really know where to begin this is what i have down
fx = 36x^2 y + 20xy^2 + 6y^3 +4y^4
fy = 12x^3 + 10x^2(2y) + 6x(3y^2) + 16y^3
then im lost on the total differential formula
DK = dk/dx (DK) + dk/dy (DY)
(where the small 'd' represents the differential symbol
am i completely lost?
If F(x,y) is a function of x and y, and x and y are themselves functions of some variable t, then we could write F(t)= F(x(t),y(t)) as a function of t and, by the chain rule, . Since the differential of a function F(t) is defined as [tex]dF= \frac{dF}{dt}dt[tex], that gives, as the "total differential"
You almost have the correct partial derivatives
is not quite right. The derivative of with respect to x is 0, not .
is correct- once you have multiplied 10(2)= 20 and 6(3)= 18.
Then, to find dK by simply writing