oh ! so is my answer incorrect ?

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- Jun 28th 2011, 09:24 AMvidhi96Re: differentiation applying two rules
oh ! so is my answer incorrect ?

- Jun 28th 2011, 09:26 AMvidhi96Re: differentiation applying two rules
here is my second example - please see if my inital steps are correct- while I get my head around what I did wrong in first example- ta

- Jun 28th 2011, 09:29 AMvidhi96Re: differentiation applying two rules
what you mean?

- Jun 28th 2011, 09:34 AMvidhi96Re: differentiation applying two rules
Ok I read what you said and I tried again- you can't fail me for trying. Please have a look

- Jun 28th 2011, 09:43 AMArchie MeadeRe: differentiation applying two rules
For that last example, you overlooked squaring the entire denominator.

What I meant earlier is that you are comfortable with the situation

where the "function nesting" is one level deep, when applying the chain rule.

$\displaystyle e^{6x}$ is one level beyond $\displaystyle e^x$

q=6x

$\displaystyle \frac{d}{dx}e^{6x}=\frac{d}{dx}e^q=\frac{dq}{dx} \frac{d}{dq}e^q$

However...

$\displaystyle v=\left(1+3x^2\right)^{\frac{1}{2}}$

has an extra stage.

Beginning with x, we have

$\displaystyle w=1+3x^2$

but then we take the square root of this

$\displaystyle v=w^{\frac{1}{2}}$

so the "nesting" is 2 levels deep, whereas it was only 1 level deep for $\displaystyle e^{6x}$

Hence

$\displaystyle \frac{d}{dx}\left(1+3x^2\right)^{\frac{1}{2}}= \frac{d}{dx}w^{\frac{1}{2}}=\frac{dw}{dx}\frac{d}{ dw}w^{\frac{1}{2}}$

$\displaystyle =\frac{dw}{dx}\left[\frac{1}{2}w^{-\frac{1}{2}}\right]$

How is that ? - Jun 28th 2011, 09:48 AMArchie MeadeRe: differentiation applying two rules
- Jun 28th 2011, 09:52 AMvidhi96Re: differentiation applying two rules
- Jun 28th 2011, 09:53 AMvidhi96Re: differentiation applying two rules
so you are telling me I am finally right

- Jun 28th 2011, 09:55 AMvidhi96Re: differentiation applying two rules
- Jun 28th 2011, 09:58 AMArchie MeadeRe: differentiation applying two rules
- Jun 28th 2011, 11:07 AMvidhi96Re: differentiation applying two rules
Ok I will do squaring and see if I can simplify in any way. However I take it rest of is ok. Is that correct? Also I know why I made mistake in "v" because I wasn't careful but since you pointed it out I think I will be extra carful in writing my steps out. Just away from the computer for next hour so when get back will send you my correction. I must say you have given me that confidence I thought I'll never have . Sincere thank you