Answer:
Step-by-step explanation: partial derivative is the differentiation of one variable e.g. X while leaving the values of the other variable e.g. Y
These four questions A, B, C and D have different functions separated by commas. I will not assume the commas to be something else like a plus sign.
A. f(x) = g'(x).k(y) , g'(x) + h(y)
f(y) = k'(y).g(x) , g(x) + h'(y)
B. f(x) = g'x (x+y)
f(y) = g'y (x+y) , h'y (y+z)
f(z) = h'z (y+z)
C. f(x) = f'x (xy) , f'x (zx)
f(y) = f'y (xy) , f'y (yz)
f(z) = f'z (yz) , f'z (zx)
D. f(x) = f'x (x) , g'(x) , h'x (x,y)
f(y) = h'x (x,y)
These are the partial derivative expressions for each variable in each function. You will need to pay a lot of attention to understand:
* while differentiating X alone, functions in Y which are separated by commas from the functions in X, are ignored totally because they are different questions
* In functions where X added to Y is in a bracket e.g. (x+y), to find the derivative of X, Y isn't thrown away because they are joined (by a plus sign) the derivative of X alone in this case would be f'x (x+y)
* f(x), just like g(x), simply means/represents a function in X hence f'(x) means the differentiation of all X-terms in that function
