#derivation question
tropic hingeBOT
- Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
- Wait patiently for a helper to come along.
- Once someone helps you, say thank you and close the thread with:
+close - Feel free to nominate the person for helper of the week in #helper-nominations
- Do not ping the mods, unless someone is breaking the rules.
- If you're happy with the help you got here, and the server overall, you can contribute financially as well:
wheat dome
If I could see the functions I would help
crimson sinew
If I could see the functions I would help
its the two that arent blacked out
wheat dome
its the two that arent blacked out
So you mean if $f$ is differentiable so is $\lambda f$ and $f^n$ for $n \geq 1$?
Is that what is being asked ?
If so you can just use the definition
fresh locustBOT
😑 rotoR
crimson sinew
yeah but theres a formula for each of them
wheat dome
And for the second one, you know that if $f:I \to J, g:J \to K$ $g$ and $f$ are différentiables so is $g \circ f$ so you can use induction
fresh locustBOT
😑 rotoR
wheat dome
Oh so you mean that you have to prove the formula ?
If so then do like I said use the definition and for the second one you can use the chain rule and proceed via induction
Wait is it $f^n$ or $f \circ f….\circ f$ n times ?
crimson sinew
some thing like that, like yk how for f+g its f'+g' but what is it supposed to be for lambda f
fresh locustBOT
😑 rotoR
crimson sinew
wdym definition
fresh locustBOT
😑 rotoR
wheat dome
Or equivalently $f’(x)=\underset{t \to x}{lim} \frac{f(t)-f(x)}{t-x}$
fresh locustBOT
😑 rotoR
wheat dome
If it’s f raised to the power n then you can use the chain rule
crimson sinew
this is seriously confusing me
its completely unrelated to the other relations weve studied so far
jovial rapids
Is help still required here?
wheat dome
its completely unrelated to the other relations weve studied so far
What relation have you studied ?
You can post the relation/formulas in French btw I can read it
crimson sinew
Is help still required here?
Yes please
wheat dome
Okay for the first one consider $g(x)=\lambda$ so $\lambda f(x)=g(x)f(x)$ then you can use the product formula
fresh locustBOT
😑 rotoR
wheat dome
For the second one you can use induction
Assuming $f^n$ is f to the power of n
Or you could use the chain rule but I’m assuming you haven’t seen it yet
fresh locustBOT
😑 rotoR
crimson sinew
No since I'm supposed to learn this lesson again this year so I'm pretty sure I'm missing a lot from it since I only studied the basics last year
Ty tho
wheat dome
No since I'm supposed to learn this lesson again this year so I'm pretty sure I'...
So do you understand what you have to do ?
wheat dome
**😑 rotoR**
With this
crimson sinew
Yeah I understand
wheat dome
Okay good then
crimson sinew
Tysm
wheat dome
Np