-600*x*(1/300+log(100+x^2)*1/(300*log(10)))*1/((1+log(100+x^2)*1/log(10))^2*(100+x^2)*log(10)*log(1/10)) если x=3 (упростите выражение)

Дано

$$\frac{- 600 x \left(\frac{\log{\left (x^{2} + 100 \right )}}{300 \log{\left (10 \right )}} + \frac{1}{300}\right)}{\left(x^{2} + 100\right) \left(\frac{\log{\left (x^{2} + 100 \right )}}{\log{\left (10 \right )}} + 1\right)^{2} \log{\left (10 \right )} \log{\left (\frac{1}{10} \right )}}$$
Подстановка условия
$$\frac{- 600 x \left(\frac{\log{\left (x^{2} + 100 \right )}}{300 \log{\left (10 \right )}} + \frac{1}{300}\right)}{\left(x^{2} + 100\right) \left(\frac{\log{\left (x^{2} + 100 \right )}}{\log{\left (10 \right )}} + 1\right)^{2} \log{\left (10 \right )} \log{\left (\frac{1}{10} \right )}}$$

((-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))

$$\frac{- 600 (3) \left(\frac{\log{\left ((3)^{2} + 100 \right )}}{300 \log{\left (10 \right )}} + \frac{1}{300}\right)}{\left((3)^{2} + 100\right) \left(\frac{\log{\left ((3)^{2} + 100 \right )}}{\log{\left (10 \right )}} + 1\right)^{2} \log{\left (10 \right )} \log{\left (\frac{1}{10} \right )}}$$

((-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))

$$\frac{- 1800 \left(\frac{1}{300} + \frac{\log{\left (3^{2} + 100 \right )}}{300 \log{\left (10 \right )}}\right)}{\left(1 + \frac{\log{\left (3^{2} + 100 \right )}}{\log{\left (10 \right )}}\right)^{2} \left(3^{2} + 100\right) \log{\left (10 \right )} \log{\left (\frac{1}{10} \right )}}$$

-(-6 — 6*log(109)/log(10))/(109*(1 + log(109)/log(10))^2*log(10)^2)

$$- \frac{- \frac{6 \log{\left (109 \right )}}{\log{\left (10 \right )}} — 6}{109 \left(1 + \frac{\log{\left (109 \right )}}{\log{\left (10 \right )}}\right)^{2} \log^{2}{\left (10 \right )}}$$
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Степени
$$\frac{600 x \left(\frac{\log{\left (x^{2} + 100 \right )}}{300 \log{\left (10 \right )}} + \frac{1}{300}\right)}{\left(x^{2} + 100\right) \left(\frac{\log{\left (x^{2} + 100 \right )}}{\log{\left (10 \right )}} + 1\right)^{2} \log^{2}{\left (10 \right )}}$$

/ / 2\
| 1 log100 + x /|
-600*x*|— + ————-|
300 300*log(10) /
——————————————
2
/ / 2\
| log100 + x /| / 2 2
|1 + ————-| * -100 — x /*log (10)
log(10) /

$$- \frac{600 x \left(\frac{\log{\left (x^{2} + 100 \right )}}{300 \log{\left (10 \right )}} + \frac{1}{300}\right)}{\left(- x^{2} — 100\right) \left(\frac{\log{\left (x^{2} + 100 \right )}}{\log{\left (10 \right )}} + 1\right)^{2} \log^{2}{\left (10 \right )}}$$
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
$$\frac{300 x \log{\left (x^{2} + 100 \right )} + 300 x \log{\left (10 \right )}}{150 \left(x^{2} + 100\right) \left(\log{\left (x^{2} + 100 \right )} + \log{\left (10 \right )}\right)^{2} \log{\left (10 \right )}}$$
Объединение рациональных выражений
$$\frac{2 x}{\left(x^{2} + 100\right) \left(\log{\left (x^{2} + 100 \right )} + \log{\left (10 \right )}\right) \log{\left (10 \right )}}$$
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Общее упрощение

2*x
———————————————
/ 2 / / 2\
100 + x /*\log(10) + log100 + x //*log(10)

$$\frac{2 x}{\left(x^{2} + 100\right) \left(\log{\left (x^{2} + 100 \right )} + \log{\left (10 \right )}\right) \log{\left (10 \right )}}$$
Соберем выражение
$$- \frac{600 x \left(\frac{\log{\left (x^{2} + 100 \right )}}{300 \log{\left (10 \right )}} + \frac{1}{300}\right)}{\left(x^{2} + 100\right) \left(\frac{\log{\left (x^{2} + 100 \right )}}{\log{\left (10 \right )}} + 1\right)^{2} \log{\left (\frac{1}{10} \right )} \log{\left (10 \right )}}$$

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 /

$$\frac{2 x}{x^{2} \log{\left (10 \right )} \log{\left (x^{2} + 100 \right )} + x^{2} \log^{2}{\left (10 \right )} + 100 \log{\left (10 \right )} \log{\left (x^{2} + 100 \right )} + 100 \log^{2}{\left (10 \right )}}$$
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Комбинаторика

2*x
———————————————
/ 2 / / 2\
100 + x /*\log(10) + log100 + x //*log(10)

$$\frac{2 x}{\left(x^{2} + 100\right) \left(\log{\left (x^{2} + 100 \right )} + \log{\left (10 \right )}\right) \log{\left (10 \right )}}$$
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) /

$$\frac{600 x \left(\frac{\log{\left (x^{2} + 100 \right )}}{300 \log{\left (10 \right )}} + \frac{1}{300}\right)}{\left(x^{2} + 100\right) \left(\frac{\log{\left (x^{2} + 100 \right )}}{\log{\left (10 \right )}} + 1\right)^{2} \log^{2}{\left (10 \right )}}$$

/ / 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) /

$$- \frac{600 x \left(\frac{\log{\left (x^{2} + 100 \right )}}{300 \log{\left (10 \right )}} + \frac{1}{300}\right)}{\left(x^{2} + 100\right) \left(\frac{\log{\left (x^{2} + 100 \right )}}{\log{\left (10 \right )}} + 1\right)^{2} \log{\left (\frac{1}{10} \right )} \log{\left (10 \right )}}$$
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