How can you differentiate y=IN(x^2+3)?

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Answer 1 · 2018-04-09T17:49:48

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You have 2 functions, $ln (x) and x^{2} + 3$ $ln(x) and x^2+3$

apply the chain rule, $u'(v)*v'$

$\frac{1}{x^2+3}*2x$

$\frac{2x}{x^2+3}$

Prove if its right?

Integrate!

$int \frac{2x}{x^2+3}dx$

use u-substitution

$u=x^2+3 -> dx = 1/(2x)du$

$int 1/u du = ln(u)$

$ln(x^2+3) +C$