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# differentiating stuff that's in brackets watch

1. apparently, 1/2(e1+e2)^2 differentiates to e1+e2

is this always the case?

e.g would 0.3(e1+e2)^2 differentiate to 0.6e1 + 0.6e2

or would 0.7(2e1+8e2)^2 differentiate to 1.4(2e1+8e2) = 2.8e1 +11.2e2?

thanks
2. apparently, 1/2(e1+e2)^2 differentiates to e1+e2

I don't know what you mean by e1 and e2, but this requires the chain rule.

Let's say (e1+e2) = u, then 1/2(e1+e2)^2 = 1/2 x u^2

Use dy/dx = dy/du x du/dx (y in terms of x)

So dy/du = u and du/dx = d(e1+e2)/dx

Say you have 1/2(x+1)^2 , this differentiates to x+1 as x+1 differentiates to 1.

If you have 1/2(2x+1)^2, this differentiates to 2(2x+1)
3. or another way of doing it, as i don't really like the chain rule:

times by the power
take one from the power
times by the differential of the things in brackets

for example-
goes to (i hope, i did have to go and choose a complicated example!)
4. sorry for not making it clearer, think of e1 and e2 as "x" and "y"... is what i wrote correct or false?
5. (Original post by Aleeece123)
or another way of doing it, as i don't really like the chain rule:

times by the power
take one from the power
times by the differential of the things in brackets

for example-
goes to (i hope, i did have to go and choose a complicated example!)
But that is the chain rule.

(Original post by redkopite)

sorry for not making it clearer, think of e1 and e2 as "x" and "y"... is what i wrote correct or false?
I don't know. Your notation is a little confusing.
What's in the brackets? What are you finding?

a(bx + c)^n

Differentiates wrt x to:

nab(bx + c)^n-1

Because u = bx + c
du/dx = b
d/dx = du/dx * d/du

But in your example, you say e1 and e2. If they are numbers, then they have no derivative. If they are terms of x, then yes, you are right. Except for your last one. It doesn't really make sense.

Then you said, think of it as x and y. Well that would be:

a(bx + cy)^n

Differentiates wrt x to:

na(b +c(dy/dx))(bx + cy)^n-1

Through implicit differentiation.

I think I've made this look very complicated to you, but you're not being very clear. I think my first example answers your question though.
6. (Original post by AnonyMatt)
But that is the chain rule.
so it is... ahh that would explain a lot! Maybe i just don't like saying "chain rule"

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