Differentiate x^2 ln(1+x^2)

Loldi9s

Loldi9s

Open question

2022-08-21

Differentiate
x 2 ln ( 1 + x 2 )
I simplified it till -
2 x 2 ln ( x )
Then I differentiate -
2 x 2 ( 1 x ( d d x x ) + ln x ( 4 x )
2 x 2 x + 4 x ln x
Where have I gone wrong ? Because the answer I am trying to achieve is
2 x 3 1 + x 2 + 2 x ln ( 1 + x 2 )

Answer & Explanation

micelarnyiz

micelarnyiz

Beginner2022-08-22Added 8 answers

Simply apply product rule :
d ( f ( x ) g ( x ) ) d x = f ( x ) g ( x ) + f ( x ) g ( x )
nascarchic839e9

nascarchic839e9

Beginner2022-08-23Added 2 answers

Your simplification is wrong: you can't do that with logarithms. Directly with the product rule:
( x 2 log ( 1 + x 2 ) ) = 2 x log ( 1 + x 2 ) + 2 x 3 1 + x 2

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