Hello, can someone help me. what the answer. thank you

Question

Given that

w(x,y,z)=8y²/(sqrtx³sqrtz²).

Use partial derivatives to find the maximum percentage error in w, if the maximum percentage error in x is 1%, the maximum percentage error in y is 2% and the maximum percentage error in z is 3%.

Answer 1

Given: |Δx/x| = 0.01 |Δy/y| = 0.02 |Δz/z| = 0.03

w(x,y,z) = 8y²/(√x³√z²) = 8y²x^-3/2z^-1

∂w/∂x = 8(-3/2)y²x^-5/2z^-1

∂w/∂y = 16yx^-3/2z^-1

∂w/∂z = -8y²x^-3/2z^-2

dw(x,y,z) = ∂w/∂x dx + ∂w/∂y dy + ∂w/∂z dz

dw/w = (-3/2) dx/x + 2dy/y -dz/z after some algebra

= -3/2 (0.01) + 2(0.02) - (0.03) = -0.005

|Δw/w| = 0.005 = 0.5%