Подробное решение
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Не могу найти шаги в поиске этой производной.
Но производная
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Теперь упростим:
Ответ:
__________ / __________ \
/ 2 | / 2 / 2 \ |
\/ 1 - 3*x |\/ 1 - 3*x *\1 + tan (x)/ 3*x*log(tan(x))|
(tan(x)) *|--------------------------- - ---------------|
| tan(x) __________ |
| / 2 |
\ \/ 1 - 3*x /
$$\left(- \frac{3 x \log{\left(\tan{\left(x \right)} \right)}}{\sqrt{- 3 x^{2} + 1}} + \frac{\sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}}\right) \tan^{\sqrt{- 3 x^{2} + 1}}{\left(x \right)}$$
/ 2 \
__________ |/ __________ \ 2 __________ |
/ 2 || / 2 / 2 \ | __________ / 2 \ / 2 2 / 2 \ |
\/ 1 - 3*x || \/ 1 - 3*x *\1 + tan (x)/ 3*x*log(tan(x))| 3*log(tan(x)) / 2 / 2 \ \1 + tan (x)/ *\/ 1 - 3*x 9*x *log(tan(x)) 6*x*\1 + tan (x)/ |
(tan(x)) *||- --------------------------- + ---------------| - ------------- + 2*\/ 1 - 3*x *\1 + tan (x)/ - ---------------------------- - ---------------- - --------------------|
|| tan(x) __________ | __________ 2 3/2 __________ |
|| / 2 | / 2 tan (x) / 2\ / 2 |
\\ \/ 1 - 3*x / \/ 1 - 3*x \1 - 3*x / \/ 1 - 3*x *tan(x)/
$$\left(2 \sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right) + \left(\frac{3 x \log{\left(\tan{\left(x \right)} \right)}}{\sqrt{- 3 x^{2} + 1}} - \frac{\sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}}\right)^{2} - \frac{\sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} - \frac{9 x^{2} \log{\left(\tan{\left(x \right)} \right)}}{\left(- 3 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{6 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{- 3 x^{2} + 1} \tan{\left(x \right)}} - \frac{3 \log{\left(\tan{\left(x \right)} \right)}}{\sqrt{- 3 x^{2} + 1}}\right) \tan^{\sqrt{- 3 x^{2} + 1}}{\left(x \right)}$$
/ 3 \
__________ | / __________ \ / __________ \ / 2 __________ \ 2 __________ 3 __________ 2 |
/ 2 | | / 2 / 2 \ | | / 2 / 2 \ | | __________ / 2 \ / 2 2 / 2 \ | 3 / 2 \ / 2 \ / 2 \ / 2 / 2 \ / 2 __________ 2 / 2 \ / 2 \ |
\/ 1 - 3*x | | \/ 1 - 3*x *\1 + tan (x)/ 3*x*log(tan(x))| | \/ 1 - 3*x *\1 + tan (x)/ 3*x*log(tan(x))| | / 2 / 2 \ 3*log(tan(x)) \1 + tan (x)/ *\/ 1 - 3*x 9*x *log(tan(x)) 6*x*\1 + tan (x)/ | 81*x *log(tan(x)) 27*x*log(tan(x)) 18*x*\1 + tan (x)/ 9*\1 + tan (x)/ 4*\1 + tan (x)/ *\/ 1 - 3*x 2*\1 + tan (x)/ *\/ 1 - 3*x / 2 / 2 \ 27*x *\1 + tan (x)/ 9*x*\1 + tan (x)/ |
(tan(x)) *|- |- --------------------------- + ---------------| + 3*|- --------------------------- + ---------------|*|- 2*\/ 1 - 3*x *\1 + tan (x)/ + ------------- + ---------------------------- + ---------------- + --------------------| - ----------------- - ---------------- - ------------------ - -------------------- - ------------------------------ + ------------------------------ + 4*\/ 1 - 3*x *\1 + tan (x)/*tan(x) - -------------------- + ---------------------|
| | tan(x) __________ | | tan(x) __________ | | __________ 2 3/2 __________ | 5/2 3/2 __________ __________ tan(x) 3 3/2 __________ |
| | / 2 | | / 2 | | / 2 tan (x) / 2\ / 2 | / 2\ / 2\ / 2 / 2 tan (x) / 2\ / 2 2 |
\ \ \/ 1 - 3*x / \ \/ 1 - 3*x / \ \/ 1 - 3*x \1 - 3*x / \/ 1 - 3*x *tan(x)/ \1 - 3*x / \1 - 3*x / \/ 1 - 3*x \/ 1 - 3*x *tan(x) \1 - 3*x / *tan(x) \/ 1 - 3*x *tan (x)/
$$\left(4 \sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \left(\frac{3 x \log{\left(\tan{\left(x \right)} \right)}}{\sqrt{- 3 x^{2} + 1}} - \frac{\sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}}\right)^{3} - \frac{4 \sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 3 \cdot \left(\frac{3 x \log{\left(\tan{\left(x \right)} \right)}}{\sqrt{- 3 x^{2} + 1}} - \frac{\sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}}\right) \left(- 2 \sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{\sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + \frac{9 x^{2} \log{\left(\tan{\left(x \right)} \right)}}{\left(- 3 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{- 3 x^{2} + 1} \tan{\left(x \right)}} + \frac{3 \log{\left(\tan{\left(x \right)} \right)}}{\sqrt{- 3 x^{2} + 1}}\right) - \frac{18 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{- 3 x^{2} + 1}} + \frac{2 \sqrt{- 3 x^{2} + 1} \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} + \frac{9 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\sqrt{- 3 x^{2} + 1} \tan^{2}{\left(x \right)}} - \frac{81 x^{3} \log{\left(\tan{\left(x \right)} \right)}}{\left(- 3 x^{2} + 1\right)^{\frac{5}{2}}} - \frac{27 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(- 3 x^{2} + 1\right)^{\frac{3}{2}} \tan{\left(x \right)}} - \frac{27 x \log{\left(\tan{\left(x \right)} \right)}}{\left(- 3 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{9 \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{- 3 x^{2} + 1} \tan{\left(x \right)}}\right) \tan^{\sqrt{- 3 x^{2} + 1}}{\left(x \right)}$$