# How to simplify after differentiation.

• May 14th 2009, 11:38 PM
dwat
How to simplify after differentiation.
Hi

I have a problem with simplifying after I differentiate, can anyone enlighten me as what are some key ways in simplifying equations

Heres my problem

h(t)=[2t-1]/sqrt(1+t)
rearranged it.

h[t]=[2t-1][1+t]^(-1/2)
Product Rule
h'[t]=2*([-1/2][1+t]^[-3/2]) + (([1+t]^[1/2])*2
now how do i go about in simplifying that? my problem is expanding the brackets with variables and powers.
Show me some necessary steps needed
• May 15th 2009, 02:58 AM
HallsofIvy
Quote:

Originally Posted by dwat
Hi

I have a problem with simplifying after I differentiate, can anyone enlighten me as what are some key ways in simplifying equations

Heres my problem

h(t)=[2t-1]/sqrt(1+t)
rearranged it.

h[t]=[2t-1][1+t]^(-1/2)
Product Rule
h'[t]=2*([-1/2][1+t]^[-3/2]) + (([1+t]^[1/2])*2

How is this the "product rule"?
(2t- 1)'= 2 and ((1+ t)^(-1/2)'= (-1/2)(1+ t)^(-3/2). The product rule gives h'= 2(1+t)^(-1/2)- (1/2)(2t-1)(1+t)^(-3/2).

To simplify that, I would recomment rewriting the roots as square roots again. Of course, (1+t)^(-3/2)= (1+t)^(-1)(1+t)^(-1/2).

$h'= \frac{2}{\sqrt{1+ t}}- \frac{2t-1}{2(1+t)\sqrt{1+t}}$

Now get common denominators and combine the fractions.
now how do i go about in simplifying that? my problem is expanding the brackets with variables and powers.
Show me some necessary steps needed[/QUOTE]
• May 15th 2009, 03:00 AM
mr fantastic
Quote:

Originally Posted by dwat
Hi

I have a problem with simplifying after I differentiate, can anyone enlighten me as what are some key ways in simplifying equations

Heres my problem

h(t)=[2t-1]/sqrt(1+t)
rearranged it.

h[t]=[2t-1][1+t]^(-1/2)
Product Rule
h'[t]=2*([-1/2][1+t]^[-3/2]) + (([1+t]^[1/2])*2 Mr F says: This is wrong.
now how do i go about in simplifying that? my problem is expanding the brackets with variables and powers.
Show me some necessary steps needed

You have not applied the product rule correctly. You should do it again, putting in every step of working.

Personally however, I'd use the quotient rule. As with carpentry, the job is always easier if you use the right tool.
• May 17th 2009, 03:28 PM
dwat
Thanks. I see where I went wrong