Author Topic: Help with differentiation! (Read 1146 times) Tweet Share

Bee49 · « **on:** July 24, 2011, 11:07:52 am »

Could someone please help me solve this? I'm really stuck

Find the derivative with respect to x:

(1 + x^2)^0.5

Thanks!

stonecold · « **Reply #1 on:** July 24, 2011, 11:17:48 am »

You need to use the chain rule.

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

$y=u^{\frac{1}{2}} = \sqrt{u}$

$u = 1 + x^2$

$\frac{du}{dx}= 2x$

$\frac{dy}{du}=\frac{1}{2\sqrt{u}}$

$\therefore \frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}= 2x \cdot \frac{1}{2\sqrt{u}} = \frac{x}{\sqrt{1 + x^2}}$

Bee49 · « **Reply #2 on:** July 24, 2011, 11:29:36 am »

Thanks! We haven't done the chain rule in school (our teacher skipped that exercise), so I'll look it up.

stonecold · « **Reply #3 on:** July 24, 2011, 11:44:54 am »

Quote from: Bee49 on July 24, 2011, 11:29:36 am

Thanks! We haven't done the chain rule in school (our teacher skipped that exercise), so I'll look it up.

If you are in year 11 then I wouldn't worry about it, but in year 12 it is vital that you can understand and apply it because a lot of problems will need it.

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Author Topic: Help with differentiation! (Read 1146 times) Tweet Share

Bee49

Help with differentiation!

stonecold

Re: Help with differentiation!

Bee49

Re: Help with differentiation!

stonecold

Re: Help with differentiation!

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