composite functions

[cobalt isle]

Hi could someone explain / walk me through this question? I don’t get it at all (this is a past test and I’m not understanding the solution either). Thank you !

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[ivory dragon]

I mean, the straightforward method is just to calculate f(f(x)) and then differentiate it directly, but I can see how that'd be pretty complicated.

That said, do you accept that g'(x) = f'(f(x)) * f'(x)?

[sudden nimbus]

you can factor out $e^{1+e^2}$ from the last step you have there

[left patrol]

!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!

[cobalt isle]

yep yep chain rule right?

[ivory dragon]

Then you simply need to calculate f'(x).

[cobalt isle]

I think I did smth wrong but idk where 😭

[split swan]

g'(x)=f'(f(x))*f'(x) using chain rule

[split swan]

in line 3, you forgot to put the squared symbol in the 2nd xe^x^2 term

[cobalt isle]

okok i finally got the answer💫 thank you all !

[split swan]

yw

[fresh arch]

@cobalt isle

<:HelpIcon:1304095958283321385>| Help Reminder

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[dry comet]

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