Question

Quotient Rule:
z^2+1/Z^(1/2)
Their answer is:
Z^(1/2)(3-z^(-2)/(2)
I can't do the simplification!
Yes z and Z was a typo only 1 variable here

Answer 1

When in doubt, Product Rule:
\[\huge z^2+z^{-\frac{1}{2}}\]

Answer 2

but if after derivative you've gotten:
\[\huge2z-\frac{1}{z^{\frac{3}{2}}}\]
the simplification involves factoring out a 1/2z to make the bottom look nice:
\[\huge 2z^{\frac{1}{2}}(z^{\frac{1}{2}})-\frac{z^{\frac{1}{2}}}{z^2}\]
\[\huge z^{\frac{1}{2}}(2z^{\frac{1}{2}}-\frac{1}{z^2})\]
....hmmm i can't get their answer either

Answer 3

assuming z and Z are just typos and that they are actually the same variable:

(z^2+1)*z^(-1/2)

z^(3/2)+ z^(-1/2)

3/2 z^(1/2)-1/2 z^(-3/2)

(3z^(2)-1)/2z^(3/2)

z^2(3-z^(-2))/2z^(3/2)

z^(1/2) (3-z^(-2))/2

Answer 4

im not sure if the "answer" is that, it seems to be an oversimplification to me that borders on complicating it.