Question

знайти похідну
$f(x) = ln(6x - 9)$
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Answer 1

Решение:

$f(x) = ln(6x-9)\\f'(x) = (ln(6x-9))' = (ln(6x-9))'*(6x-9)' = \frac{1}{6x-9}*((6x)'-(9)') = \frac{1}{6x-9}*(6(x)'-0) = \frac{1}{6x-9}*(6*1-0) = \frac{1}{6x-9}*(6-0) = \frac{1}{6x-9}*6 = \frac{6}{6x-9} = \frac{6}{3(2x-3)} = \frac{2}{2x-3}$

Ответ: $f'(x) = \frac{2}{2x-3}$