need help with maths question - partial differentiation!!!?

Question

hi could you please help me partially differentitate this into x and y

z=20x - 2xy - y2 ( the 2 on y2 means squared).


thankyou

Answer 1

easy

in case you want to paritally differnetiate wrt x y is constant

z = 20x - 2xy - y2

dz/dx = 20 - 2y ( as y is constnt dy/dx = 0)

if partial differentiation wrt y then x is constant

dz/dy = -2x - 2y (dx/dy = 0)

kindly excuse for the symbol dz/dx

Answer 2

When you partially differentiate z with respect to x, treat y as if it were a constant. Thus, δz/δx=20-2y=2(10-y)

Similarly, when you differentiate z with respect to y, you treat x as if it were a constant. Thus,

δz/δy=-2x-2y= -2(x+y)

I hope this helps!

Answer 3

z= 20x -2xy -y^2

first,we will differentiate z with respect to x

(δz/δx) = 20 -2y,

(since y is a constant,its derivative with respect to x is 0)

now, we will differentiate z with respect to y

(δz/δy) = -2x-2y,

(since x is a constant, its derivative with respect to y is 0)

in order to distinguish from ordinary differentiation (d) we use the greek letter (δ) for partial differentiation

Answer 4

dz/dx = 20 - 2y

dz/dy = -2x - 2y

Answer 5

Go to a maths tutor if you don't know.