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Differentiation

1. If f is differentiable at x, find expressions for the derivatives of the following functions:
(a) x + f(x)
(b) [f(x)]^2 − x
(c) [f(x)]^4
(d) x^2f(x) + [f(x)]^3


Any ideas on how to do this? (Awful lecturer)
Reply 1
Avatar for davros
davros
16
Original post by Nilsdejongh
1. If f is differentiable at x, find expressions for the derivatives of the following functions:
(a) x + f(x)
(b) [f(x)]^2 − x
(c) [f(x)]^4
(d) x^2f(x) + [f(x)]^3


Any ideas on how to do this? (Awful lecturer)


Not entirely sure how much rigour is expected here, but my immediate reaction to all of these is "chain rule" (or some combination of chain rule and product rule) - i.e. it's just applying the rules you learned at A level when you naively assumed that everything was differentiable and just went ahead and did it!
Reply 2
Avatar for Nilsdejongh
Nilsdejongh
OP
Original post by davros
Not entirely sure how much rigour is expected here, but my immediate reaction to all of these is "chain rule" (or some combination of chain rule and product rule) - i.e. it's just applying the rules you learned at A level when you naively assumed that everything was differentiable and just went ahead and did it!


so for the first one it'd sort of be 1 + f'(x)?
Reply 3
Avatar for TeeEm
TeeEm
19
Original post by Nilsdejongh
so for the first one it'd sort of be 1 + f'(x)?


assuming no proof from first principles is needed, that is correct.
Reply 4
Avatar for davros
davros
16
Original post by Nilsdejongh
so for the first one it'd sort of be 1 + f'(x)?



Original post by TeeEm
assuming no proof from first principles is needed, that is correct.


Agreed.

Seems a strange sort of question tbh :smile:

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