Find G'(x) if G(x) (integral with a to x) 2lnydy???

Question

anonymous · Answer

$$G(x) \int\limits_{a}^{x}2lnydy $$

myininaya · Answer

$$G(x)=\int\limits\limits_{a}^{x}f(y) dy = F(y)|_{a}^{x} =F(x)-F(a)   $$
F(a) is a constant so ...
$$(G(x))'=(F(x)-F(a))'=(F(x))'  $$
But F'=f so we have
$$G'(x)=F'(x)=f(x)$$

anonymous · Answer

so what would I put in for the x and a?

myininaya · Answer

G'(x)=f(x) where f is the machine inside your integral just replace the y with x.

myininaya · Answer

Why do we want to put something there to replace them?
We are trying to find the derivative of the above expression.

anonymous · Answer

so the answer would be 2lnxdx?

myininaya · Answer

not the dx

anonymous · Answer

So just 2lnx? and thats it?

myininaya · Answer

yep

anonymous · Answer

would it look like $$\int\limits_{a}^{x}(2lnx)dx?$$

myininaya · Answer

?

myininaya · Answer

No we were finding the derivative of G

anonymous · Answer

So just 2lnx? when I type it into my homework it makes it look like 2ln(x), is that okay?

myininaya · Answer

Yes. Did you not understand the first post? If you don't please tell me what you don't understand so I can better help you.

anonymous · Answer

I think it just confused me about the parenthesis, but if its okay as 2ln(x) than I think I understand! Thanks for your help it was right!! :)