y = 4 x^-4 + 3 x^.5
dy/dx = (-20) x^-5 + 1.5 x^-.5
delta y=(-20/x^5)delta x+(1.5/x^.5)delta x
if x = 4 then x^5 = 1024 and x^.5 = 2
so
delta y =(-20/1024 + 1.5/2 ) .5
= .365
=========================
now exact
y1 = .003906 + 6 = 6.003906
y2 = .009755 + 6.3640
y2-y1 = delta y = .360
not bad
Find dy for the given values of x and Δx.
y=4/x^4+3√x; x=4, Δx=.5
4 answers
dy/dx = -16 x^-5 + 1.5 x^-.5
so
dy/dx here = -.0156 + .75 = .7344
so
dy = .7344* .5 = .367
so
dy/dx here = -.0156 + .75 = .7344
so
dy = .7344* .5 = .367
Where did you made error on the first one? did you typed wrong numbers or problem.
if y = x^-4
dy/dx = -4 x^-5
not
-5 x^-5
dy/dx = -4 x^-5
not
-5 x^-5