# Derivative help

#### Draggu

1. The problem statement, all variables and given/known data
(1/2)t^2[(2$$\sqrt{t}$$)-(1/$$\sqrt{t}$$)]

2. Relevant equations

3. 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')

#### Tom Mattson

Staff Emeritus
Gold Member
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)]

#### Tom Mattson

Staff Emeritus
Gold Member
=(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)

#### Tom Mattson

Staff Emeritus
Gold Member
What do i do then? ;s
Just differentiate term by term.

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

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