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If you already know how to obtain derivatives, these should be mind blowingly simple,

Fx means you disregard all other variables exccept "x" of course, as constant and derive the equation.

example:

Fx = ln(yz^2) + y.(1/x) ;here The derivative of the natural logarithm is given by d/dx(lnx) = 1/x

Fxx means do it twice,

Fxx = y.(-1/zx^2) ;notice here that because we fixed all other variables except "x" the whole

"ln(yz^2)" is cancelled out as constant.

Fxy means First variate only "x" for derivatives and then "y",

Fxy = Fy(Fx);

Fxy = Fy(ln(yz^2) + y.(1/zx))

Fxy = (1/yz^2) + 1/zx

I'm sure you would have figured it out by now.

deriviative is 4x-(5xy'+5y+xy) use product rule for 5xy, use x's actually spinoff and write spinoff of y as y' and go away it on my own after that. in case you didnt understand product rule is derivitive of one term cases the different plus the derivitive of the different term cases the 1st term thats no longer consumer-friendly to understand so der. of xy is x'y+xy' that's generally written as y+xy' in terms of x when you consider that spinoff of x is a million you additionally can use the chain rule after pulling an x out so as that that's x(2x-5y) wich then you particularly could use the product rule besides and get (2x-5y)+x(2+5y') that's 4x -5y+2x+5y' which with slightly extra artwork you are able to teach equals the spinoff of the 1st occasion i confirmed you.

The natural logs work the exact same way as in Calc I.

d/dx [ln(f(x))] = f'(x) / f(x)