Дано
$$frac{- 600 x left(frac{log{left (x^{2} + 100 right )}}{300 log{left (10 right )}} + frac{1}{300}right)}{left(x^{2} + 100right) left(frac{log{left (x^{2} + 100 right )}}{log{left (10 right )}} + 1right)^{2} log{left (10 right )} log{left (frac{1}{10} right )}}$$
Подстановка условия
$$frac{- 600 x left(frac{log{left (x^{2} + 100 right )}}{300 log{left (10 right )}} + frac{1}{300}right)}{left(x^{2} + 100right) left(frac{log{left (x^{2} + 100 right )}}{log{left (10 right )}} + 1right)^{2} log{left (10 right )} log{left (frac{1}{10} right )}}$$
((-600*(3))*(1/300 + log(100 + (3)^2)/(300*log(10))))/((((1 + log(100 + (3)^2)/log(10))^2*(100 + (3)^2))*log(10))*log(1/10))
$$frac{- 600 (3) left(frac{log{left ((3)^{2} + 100 right )}}{300 log{left (10 right )}} + frac{1}{300}right)}{left((3)^{2} + 100right) left(frac{log{left ((3)^{2} + 100 right )}}{log{left (10 right )}} + 1right)^{2} log{left (10 right )} log{left (frac{1}{10} right )}}$$
((-1800)*(1/300 + log(100 + 3^2)/(300*log(10))))/((((1 + log(100 + 3^2)/log(10))^2*(100 + 3^2))*log(10))*log(1/10))
$$frac{- 1800 left(frac{1}{300} + frac{log{left (3^{2} + 100 right )}}{300 log{left (10 right )}}right)}{left(1 + frac{log{left (3^{2} + 100 right )}}{log{left (10 right )}}right)^{2} left(3^{2} + 100right) log{left (10 right )} log{left (frac{1}{10} right )}}$$
-(-6 – 6*log(109)/log(10))/(109*(1 + log(109)/log(10))^2*log(10)^2)
$$- frac{- frac{6 log{left (109 right )}}{log{left (10 right )}} – 6}{109 left(1 + frac{log{left (109 right )}}{log{left (10 right )}}right)^{2} log^{2}{left (10 right )}}$$
Степени
$$frac{600 x left(frac{log{left (x^{2} + 100 right )}}{300 log{left (10 right )}} + frac{1}{300}right)}{left(x^{2} + 100right) left(frac{log{left (x^{2} + 100 right )}}{log{left (10 right )}} + 1right)^{2} log^{2}{left (10 right )}}$$
/ / 2
| 1 log100 + x /|
-600*x*|— + ————-|
300 300*log(10) /
—————————————–
2
/ / 2
| log100 + x /| / 2 2
|1 + ————-| * -100 – x /*log (10)
log(10) /
$$- frac{600 x left(frac{log{left (x^{2} + 100 right )}}{300 log{left (10 right )}} + frac{1}{300}right)}{left(- x^{2} – 100right) left(frac{log{left (x^{2} + 100 right )}}{log{left (10 right )}} + 1right)^{2} log^{2}{left (10 right )}}$$
Численный ответ
113.167018206968*x*(0.00333333333333333 + 0.00144764827301084*log(100 + x^2))/((1.0 + 0.434294481903252*log(100 + x^2))^2*(100.0 + x^2))
Рациональный знаменатель
$$frac{300 x log{left (x^{2} + 100 right )} + 300 x log{left (10 right )}}{150 left(x^{2} + 100right) left(log{left (x^{2} + 100 right )} + log{left (10 right )}right)^{2} log{left (10 right )}}$$
Объединение рациональных выражений
$$frac{2 x}{left(x^{2} + 100right) left(log{left (x^{2} + 100 right )} + log{left (10 right )}right) log{left (10 right )}}$$
Общее упрощение
2*x
——————————————–
/ 2 / / 2
100 + x /*log(10) + log100 + x //*log(10)
$$frac{2 x}{left(x^{2} + 100right) left(log{left (x^{2} + 100 right )} + log{left (10 right )}right) log{left (10 right )}}$$
Соберем выражение
$$- frac{600 x left(frac{log{left (x^{2} + 100 right )}}{300 log{left (10 right )}} + frac{1}{300}right)}{left(x^{2} + 100right) left(frac{log{left (x^{2} + 100 right )}}{log{left (10 right )}} + 1right)^{2} log{left (frac{1}{10} right )} log{left (10 right )}}$$
2*x
——————————————————————————————————————————————————————————-
2 2 / 2 / 2 / 2
100*log (10) + x *log (10) + log(10)*log100 + x // + log(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)*log100 + x /
$$frac{2 x}{x^{2} left(log{left (10 right )} log{left (x^{2} + 100 right )} + log^{2}{left (10 right )}right) + log{left (10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 right )} log{left (x^{2} + 100 right )} + 100 log^{2}{left (10 right )}}$$
Общий знаменатель
2*x
———————————————————————————
2 2 2 / 2 2 / 2
100*log (10) + x *log (10) + 100*log(10)*log100 + x / + x *log(10)*log100 + x /
$$frac{2 x}{x^{2} log{left (10 right )} log{left (x^{2} + 100 right )} + x^{2} log^{2}{left (10 right )} + 100 log{left (10 right )} log{left (x^{2} + 100 right )} + 100 log^{2}{left (10 right )}}$$
Комбинаторика
2*x
——————————————–
/ 2 / / 2
100 + x /*log(10) + log100 + x //*log(10)
$$frac{2 x}{left(x^{2} + 100right) left(log{left (x^{2} + 100 right )} + log{left (10 right )}right) log{left (10 right )}}$$
Раскрыть выражение
/ / 2
| 1 log100 + x /|
600*x*|— + ————-|
300 300*log(10) /
—————————————-
2
/ / 2
| log100 + x /| / 2 2
|1 + ————-| *100 + x /*log (10)
log(10) /
$$frac{600 x left(frac{log{left (x^{2} + 100 right )}}{300 log{left (10 right )}} + frac{1}{300}right)}{left(x^{2} + 100right) left(frac{log{left (x^{2} + 100 right )}}{log{left (10 right )}} + 1right)^{2} log^{2}{left (10 right )}}$$
/ / 2
| 1 log100 + x /|
-600*x*|— + ————-|
300 300*log(10) /
————————————————-
2
/ / 2
| log100 + x /| / 2
|1 + ————-| *100 + x /*log(10)*log(1/10)
log(10) /
$$- frac{600 x left(frac{log{left (x^{2} + 100 right )}}{300 log{left (10 right )}} + frac{1}{300}right)}{left(x^{2} + 100right) left(frac{log{left (x^{2} + 100 right )}}{log{left (10 right )}} + 1right)^{2} log{left (frac{1}{10} right )} log{left (10 right )}}$$
