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Help with differentiating

Hi, could someone give me some hints as to how to differentiate

L=x2+a2 L=\sqrt{x^2+a^2} (where a is a constant)

I don't really know where to start...
Original post by lerjj
Hi, could someone give me some hints as to how to differentiate

L=x2+a2 L=\sqrt{x^2+a^2} (where a is a constant)

I don't really know where to start...


Have you learnt the chain rule

Remember x2+a2=(x2+a2)12\sqrt{x^2+a^2} = (x^2+a^2)^{\frac{1}{2}}
Reply 2
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lerjj
OP
13
Original post by TenOfThem
Have you learnt the chain rule

Remember x2+a2=(x2+a2)12\sqrt{x^2+a^2} = (x^2+a^2)^{\frac{1}{2}}


I kinda have, but I think I'm using it wrong. Could you explain how it works quickly?
Original post by lerjj
I kinda have, but I think I'm using it wrong. Could you explain how it works quickly?


Sure

Here is an example

ddx(2x3+5)4\dfrac{d}{dx}(2x^3+5)^4

You need to differentiate the function ()4()^4 giving 4()34()^3

Then you need to differentiate the function inside the bracket giving 6x26x^2

Then multiply these together

So

ddx(2x3+5)4=24x2(2x3+5)3\dfrac{d}{dx}(2x^3+5)^4 = 24x^2(2x^3+5)^3
Reply 4
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lerjj
OP
13
Original post by TenOfThem
Sure

Here is an example

ddx(2x3+5)4\dfrac{d}{dx}(2x^3+5)^4

You need to differentiate the function ()4()^4 giving 4()34()^3

Then you need to differentiate the function inside the bracket giving 6x26x^2

Then multiply these together

So

ddx(2x3+5)4=24x2(2x3+5)3\dfrac{d}{dx}(2x^3+5)^4 = 24x^2(2x^3+5)^3


Ok, so:

L=(x2+a2)1/2[br]dLdx=12(x2+a2)−12×2x[br][br]dLdx=x(x2+a2)−12[br] L=(x^2+a^2)^{1/2}[br]\dfrac{dL}{dx} =\dfrac{1}{2} (x^2+a^2)^{-\frac{1}{2}} \times 2x [br][br]\dfrac{dL}{dx}=x(x^2+a^2)^{-\frac{1}{2}}[br]
Original post by lerjj
Ok, so:

L=(x2+a2)1/2[br]dLdx=12(x2+a2)−12×2x[br][br]dLdx=x(x2+a2)−12[br] L=(x^2+a^2)^{1/2}[br]\dfrac{dL}{dx} =\dfrac{1}{2} (x^2+a^2)^{-\frac{1}{2}} \times 2x [br][br]\dfrac{dL}{dx}=x(x^2+a^2)^{-\frac{1}{2}}[br]


Yep
Reply 6
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lerjj
OP
13
Original post by TenOfThem
Yep


Thank you!
Original post by lerjj
Thank you!


np

I would suggest giving the answer in the same format as the question

xx2+a2\dfrac{x}{\sqrt{x^2+a^2}}

but that is just cosmetic

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