- #1
BOAS
- 553
- 19
Homework Statement
Hello,
I have an answer to my question but I'm not sure if I've simplified it correctly or if it can boil down further.
differentiate;
y = [itex]\frac{z^{3}-z}{\sqrt{z}}[/itex]
Homework Equations
Quotient rule
The Attempt at a Solution
let u = z3 - z
let v = z1/2
du/dx = 3z2 - 1
dv/dx = 1/2 z-1/2
dy/dx = [itex]\frac{z^{1/2}(3z^{2}-1) - (z^{3}-z)1/2z^{-1/2}}{(z^{1/2})^{2}}[/itex]
dy/dx = [itex]\frac{((3z^{2})(z^{1/2}) - z^{1/2}) - (z^{3})(1/2z^{-1/2})-z(z^{-1/2})}{z}[/itex]
dy/dx = [itex]\frac{(3z^{5/2} - z^{1/2}) - (1/2z^{5/2} - z^{1/2})}{z}[/itex]
dy/dx = [itex]\frac{5/2 z^{5/2}}{z}[/itex]
Thanks!