Derivative Question?

**mrsenim** · September 4th 2010, 07:04 AM

Hi All!

I am new to this topic and not sure if it is correct place to post this.

I know simple derivative like $x^3-x-1$ . For $x^3$ we multiply it by power and subtract 1 from power which is equal to $3x^2$ , x will become 1 and derivative of 1 is 0 so answer is

$3x^2-1$

Don't know how to calculate derivative of
$Derivative Question?-math.gif$
Any help please?

Another thing, where to download Latex.pdf? this link doesn't work.

Thanks in advance

**e^(i*pi)** · September 4th 2010, 07:10 AM

Originally Posted by mrsenim

Hi All!

I am new to this topic and not sure if it is correct place to post this.

I know simple derivative like $x^3-x-1$ . For $x^3$ we multiply it by power and subtract 1 from power which is equal to $3x^2$ , x will become 1 and derivative of 1 is 0 so answer is

$3x^2-1$

Don't know how to calculate derivative of
$y = \frac{1}{\sqrt{x+1}}$
Any help please?

Another thing, where to download Latex.pdf? this link doesn't work.

Thanks in advance

Chain rule works best here IMO.

Let $u = x+1$ . This should be pretty easy to solve for $\frac{du}{dx}$

Thus we get $y = \frac{1}{\sqrt{u}}$ .

Remembering the laws of exponents this is equal to $y = u^{-1/2}$ which differentiates in the same way as the positive integers so you can find $\frac{dy}{du}$ .

Here's where the chain rule comes in:

$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$

You should have and expression for both those terms

**Prove It** · September 4th 2010, 07:11 AM

$\frac{1}{\sqrt{x + 1}} = (x + 1)^{-\frac{1}{2}}$ .

Now you need to use the Chain Rule.

**mrsenim** · September 4th 2010, 07:48 AM

Originally Posted by Prove It

$\frac{1}{\sqrt{x + 1}} = (x + 1)^{-\frac{1}{2}}$ .

Now you need to use the Chain Rule.

I tried to solve it as follows

$\frac{1}{\sqrt{x + 1}} = (x + 1)^{-\frac{1}{2}}$

Now multiplying by -1/2 and subtracting 1 from power

$= {-\frac{1}{2}}[(x + 1)^{-\frac{3}{2}}]$

$= {-\frac{1}{2}}[\frac{1}{(x + 1)^{\frac{3}{2}}}]$

Is it correct?

Where to download latex.pdf? Thanks!

Don't know what is chain rule.

**e^(i*pi)** · September 4th 2010, 08:19 AM

Originally Posted by mrsenim

I tried to solve it as follows

$\frac{1}{\sqrt{x + 1}} = (x + 1)^{-\frac{1}{2}}$

Now multiplying by -1/2 and subtracting 1 from power

$= {-\frac{1}{2}}[(x + 1)^{-\frac{3}{2}}]$

$= {-\frac{1}{2}}[\frac{1}{(x + 1)^{\frac{3}{2}}}]$

Is it correct?

Where to download latex.pdf? Thanks!

Don't know what is chain rule.

In that case you managed to use the chain rule without knowing because your answer is correct

The reason is because in this case you only needed to multiply by the derivative of (x+1) which is 1

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