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Mertsj
 3 years ago
Derivative question
Mertsj
 3 years ago
Derivative question

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myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0Let F be the antiderivative of \[f(x)=\frac{u^21}{u^2+1}\] Now we have \[[g(x)]'=[F(x)_{2x}^{3x}]=[F(3x)F(2x)]'=(3x)'f(3x)(2x)'f(2x)\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0that chain rule stuff is the best! :)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0so we have \[3 \cdot \frac{(3x)^21}{(3x)^2+1}2 \cdot \frac{(2x)^21}{(2x)^2+1}\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0\[3 \cdot \frac{9x^21}{9x^2+1}2 \cdot \frac{4x^21}{4x^2+1}\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2\[\int _a^{2x}\frac{u^21}{u^2+1}du+\int_a^{3x}\frac{u^21}{u^2+1}du\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2dang did that take me a long time to type now chain rule

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0yes it did satellite :)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2i am tired, time for bed. gnight

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0me too we are going to bed

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3\[g'(x)=\frac{2(4x^21)}{4x^2+1}+\frac{3(9x^21)}{9x^2+1}\]

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3I don't get the 2 and the 3

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0:do you understand what I did?

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3I thought the u^21/u^2+1 would be the derivative and all I had to do was plug in the interval endpoints.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0\[g(x)=\int\limits_{2x}^{3x}f(u) du=F(u)_{2x}^{3x}=F(3x)F(2x)\] Do you understand this part?

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3Why isn't f(u) the g'(x)?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0no \[g(x)=F(3x)F(2x)\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0g is the integral from 2x to 3x of f(u) with respect to u

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0now since we know that \[g(x)=F(3x)F(2x)\] we can differentiate both sides

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3Ok. I get that and I understand what you wrote about F(3x)F(2x)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0\[g'(x)=(3x)'f(3x)(2x)'f(2x)\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0i used chain rule for this

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0\[g'(x)=3 f(3x)2 f(2x)\] since (3x)'=3 and (2x)'=2

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3And what happened to F(x)?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0well (F(3x))'=(3x)'f(3x) by chain rule

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0remember we differentiate both sides so we could find g'

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3Yep. Ok. I think i can figure it out now. thank you very much and how did you get so smart?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0i'm a little smart not much

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0well i'm not really smart lol

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3thanks to you and sleep well...

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0thanks i'm going to sleep for reals i'm so tired by the way satellite likes to do these types of problems another way but i love my way

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0he likes to split the integral at a constant

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.0and then use the other part of the fundamental thm of calculus

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.3Satellite is very smart also. Do you know him personally?
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