How do you differentiate if u = 2x + 4 and du = 2dx?

[jay1234]

How do you differentiate if u = 2x = 4 and du = 2dx?

I don't know how to get du, what steps are required to get du. Also, I have another question. I'm very confuse on how to use the chain rule. Can someone give me a simple explanation because the book isn't very clear on that. Thank You!

 

[galactus]

Please be more specific. What does u=2x=4 mean?. I assume you subbed in 2 for x?.

Think of the chain rule as differentiating the inside and the outside of a function.

Say you have \(\displaystyle (x^{2}+2x+1)^{3}\)

Differentiate the outside and get \(\displaystyle 3(x^{2}+2x+1)^{2}\)

Differentiate the inside of the parentheses and get \(\displaystyle 2x+2\)

Multiply and get \(\displaystyle 3(x^{2}+2x+1)^{2}(2x+2)=6(x+1)(x^{2}+2x+1)^{2}\)

That's a 'nutshell' explanation.

 

[jay1234]

I'm sorry, I meant u=2x+4

I get the chain rules, or most of it.

So in the chain rules you have to keep differentiating and multiply it by it's original function until it's not Differentiable anymore?

lets just say for argument purposes, that 2x+2 actually came out to be 2x^2+2 do I have to differentiate the part I just differentiated? I hope you know what I'm trying to say here.

 

[jay1234]

I think I got it. for u = 2x+4 you use the power rules and comes out to be du=2 dx

is this correct?