Derivative Help: t^2[2\sqrt{t} - 1/\sqrt{t}]

[Draggu]

Homework Statement

(1/2)t^2[(2$$\sqrt{t}$$)-(1/$$\sqrt{t}$$)]

Homework Equations

The Attempt at a Solution

No matter what I do I get the wrong answer
Things I have tried:
-Expanding the problem, then with the derivatives use the product rule (f)(g') + (g)(f')

 

[quantumdude]

Let's see what you did. Then we can point out where you're going wrong.

 

[Draggu]

=(1/2)t^2[(2t^(1/2)) - (t^(-1/2))]
=t^(5/2) - (1/2)^(3/2)
Use product rule

= ((5/2)t^(3/2))*((-1/2t)^(3/2)) + ((-3/4t)^(1/2))*(t^(5/2))
=(-5/4)t^3 + (-3/4)t^3
= -7/4t^3

Evidently wrong.

The correct answer on the sheet is [($$\sqrt{t}$$(10t-3)/(4)]

 

[quantumdude]

=(1/2)t^2[(2t^(1/2)) - (t^(-1/2))]
=t^(5/2) - (1/2)^(3/2)

That should be $t^{5/2}-\frac{1}{2}t^{3/2}$ (you're missing the $t$ in the second term).

Use product rule

Why? You don't have a product anymore! Just differentiate term by term.

 

[Draggu]

That should be $t^{5/2}-\frac{1}{2}t^{3/2}$ (you're missing the $t$ in the second term).



Why? You don't have a product anymore! Just differentiate term by term.

What do i do then? ;s

I'm stuck with t^(5/2) - (1/2)t^(3/2)

 

[quantumdude]

What do i do then? ;s

Just differentiate term by term.

Surely you know how to differentiate $at^n$ with respect to $t$, right?