Say f(x)=ln(1+2x+2x^2) or g(x)=tan(2x^(4)−x).Using the definition leads to messy derivatives almost immediately.If it was some simple rational function,for example,i would try to use Maclaurin Series of 1/1+x or 1/1−x . Think of any shortcut for listed above functions.

Hope Hancock 2022-10-03 Answered
Say f ( x ) = ln ( 1 + 2 x + 2 x 2 ) or g ( x ) = tan ( 2 x 4 x ).Using the definition leads to messy derivatives almost immediately.If it was some simple rational function,for example,i would try to use Maclaurin Series of 1 1 + x or 1 1 x and then manipulate it to get result
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Answers (1)

trutdelamodej0
Answered 2022-10-04 Author has 11 answers
keep substitution in mind. It may not give the whole infinite series, but you will usually get the first several terms. So,
1 1 + t = 1 t + t 2 t 3 + t 4 t 5
log ( 1 + t ) = t t 2 2 + t 3 3 t 4 4
Taking t = 2 x + 2 x 2 correctly gives the first few terms of log ( 1 + 2 x + 2 x 2 ) ,, up to x 4
log ( 1 + 2 x + 2 x 2 ) = 2 x 4 x 3 3 + 2 x 4
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