/ 3 \ atan\7*x - 1/ -------------- sin(9*x) 175 / / 2\\ E \x + 2*log\5*x // + ---- pi
дифференцируем почленно:
Не могу найти шаги в поиске этой производной.
Но производная
Производная постоянной равна нулю.
В результате:
Теперь упростим:
Ответ:
/ 3 \ atan\7*x - 1/ -------------- / / 4\ / 3 \ \ sin(9*x) |/ / 3 \ 2 \ |1 + -|*atan\7*x - 1/ | / / 2\\ || 9*atan\7*x - 1/*cos(9*x) 21*x | / / 2\\ \ x/ | \x + 2*log\5*x // *||- ------------------------- + --------------------------|*log\x + 2*log\5*x // + --------------------------| || 2 / 2\ | / / 2\\ | || sin (9*x) | / 3 \ | | \x + 2*log\5*x //*sin(9*x)| \\ \1 + \7*x - 1/ /*sin(9*x)/ /
/ 2 \ |/ / 4\ / 3\\ | || / 2 / 3\ \ |1 + -|*atan\-1 + 7*x /| / 2 / 3\ \ | / 3\ || | 7*x 3*atan\-1 + 7*x /*cos(9*x)| / / 2\\ \ x/ | / 4\ | 7*x 3*atan\-1 + 7*x /*cos(9*x)| | atan\-1 + 7*x / ||3*|---------------- - --------------------------|*log\x + 2*log\5*x // + -----------------------| 2 3*|1 + -|*|---------------- - --------------------------| | --------------- || | 2 sin(9*x) | / 2\ | / 4\ / 3\ \ x/ | 2 sin(9*x) | 2 / 4\ / 4\ / 3\ | sin(9*x) || | / 3\ | x + 2*log\5*x / | / 4 / 3\ 2 / 3\ 2 \ |1 + -| *atan\-1 + 7*x / / 3\ | / 3\ | 21*x *|1 + -| 9*|1 + -|*atan\-1 + 7*x /*cos(9*x)| / / 2\\ |\ \1 + \-1 + 7*x / / / | / 3\ 14*x 294*x *\-1 + 7*x / 54*cos (9*x)*atan\-1 + 7*x / 126*x *cos(9*x) | / / 2\\ \ x/ 4*atan\-1 + 7*x / \1 + \-1 + 7*x / / \ x/ \ x/ | \x + 2*log\5*x // *|--------------------------------------------------------------------------------------------------- + 3*|27*atan\-1 + 7*x / + ---------------- - ------------------- + ---------------------------- - ---------------------------|*log\x + 2*log\5*x // - ------------------------ - -------------------- + --------------------------------------------------------- + ------------------------------------ - ----------------------------------| | sin(9*x) | 2 2 2 / 2\ | 2 2 / / 2\\ / 2\ / 2\ / / 2\\ | | | / 3\ / 2\ sin (9*x) | / 3\ | | / / 2\\ x *\x + 2*log\5*x // x + 2*log\5*x / | / 3\ | / / 2\\ \x + 2*log\5*x //*sin(9*x) | | | 1 + \-1 + 7*x / | / 3\ | \1 + \-1 + 7*x / /*sin(9*x)| \x + 2*log\5*x // \1 + \-1 + 7*x / /*\x + 2*log\5*x // | \ \ \1 + \-1 + 7*x / / / / ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ sin(9*x)
/ / / 2 / 3\ \ \ \ | | / 4\ | 7*x 3*atan\-1 + 7*x /*cos(9*x)| | | | | 2 3*|1 + -|*|---------------- - --------------------------| | | | 3 / / 4\ / 3\\ | / 4\ / 3\ \ x/ | 2 sin(9*x) | 2 / 4\ / 4\ / 3\ | | |/ / 4\ / 3\\ | / 2 / 3\ \ |1 + -|*atan\-1 + 7*x /| | / 4 / 3\ 2 / 3\ 2 \ |1 + -| *atan\-1 + 7*x / / 3\ | / 3\ | 21*x *|1 + -| 9*|1 + -|*atan\-1 + 7*x /*cos(9*x)| / 4 / 3\ 2 / 3\ 2 \ | || / 2 / 3\ \ |1 + -|*atan\-1 + 7*x /| / 2 / 3\ \ 2 / 2 / 3\ \ | | 7*x 3*atan\-1 + 7*x /*cos(9*x)| / / 2\\ \ x/ | | | / 3\ 14*x 294*x *\-1 + 7*x / 54*cos (9*x)*atan\-1 + 7*x / 126*x *cos(9*x) | / / 2\\ \ x/ 4*atan\-1 + 7*x / \1 + \-1 + 7*x / / \ x/ \ x/ | / 4\ | / 3\ 14*x 294*x *\-1 + 7*x / 54*cos (9*x)*atan\-1 + 7*x / 126*x *cos(9*x) | | / 3\ || | 7*x 3*atan\-1 + 7*x /*cos(9*x)| / / 2\\ \ x/ | | 7*x 3*atan\-1 + 7*x /*cos(9*x)| / 4\ | 7*x 3*atan\-1 + 7*x /*cos(9*x)| 3*|3*|---------------- - --------------------------|*log\x + 2*log\5*x // + -----------------------|*|3*|27*atan\-1 + 7*x / + ---------------- - ------------------- + ---------------------------- - ---------------------------|*log\x + 2*log\5*x // - ------------------------ - -------------------- + --------------------------------------------------------- + ------------------------------------ - ----------------------------------| 6*|1 + -|*|27*atan\-1 + 7*x / + ---------------- - ------------------- + ---------------------------- - ---------------------------| | atan\-1 + 7*x / ||3*|---------------- - --------------------------|*log\x + 2*log\5*x // + -----------------------| 12*|---------------- - --------------------------| 3*|1 + -| *|---------------- - --------------------------| 3 | | 2 sin(9*x) | / 2\ | | | 2 2 2 / 2\ | 2 2 / / 2\\ / 2\ / 2\ / / 2\\ | \ x/ | 2 2 2 / 2\ | 2 2 | --------------- || | 2 sin(9*x) | / 2\ | / 2 \ | 2 sin(9*x) | \ x/ | 2 sin(9*x) | / 4\ / 3\ | | / 3\ | x + 2*log\5*x / | | | / 3\ / 2\ sin (9*x) | / 3\ | | / / 2\\ x *\x + 2*log\5*x // x + 2*log\5*x / | / 3\ | / / 2\\ \x + 2*log\5*x //*sin(9*x) | | / 3\ / 2\ sin (9*x) | / 3\ | | / 4\ / 3\ 2 / 4\ / 4\ / 3\ / 4\ 4 / 4\ / 3\ / 4\ / 3\ 2 / 4\ / 3\ 2 / 4\ | sin(9*x) || | / 3\ | x + 2*log\5*x / | | 6 2 3 / 3\ 3 / 3\ / 3\ 6 / 3\ 2 2 4 / 3\ | | / 3\ | | / 3\ | 2*|1 + -| *atan\-1 + 7*x / \ \1 + \-1 + 7*x / / / | | 1 + \-1 + 7*x / | / 3\ | \1 + \-1 + 7*x / /*sin(9*x)| \x + 2*log\5*x // \1 + \-1 + 7*x / /*\x + 2*log\5*x // | | 1 + \-1 + 7*x / | / 3\ | \1 + \-1 + 7*x / /*sin(9*x)| / 3\ 81*|1 + -|*atan\-1 + 7*x / 42*x *|1 + -| 12*|1 + -|*atan\-1 + 7*x / 42*x*|1 + -| 882*x *|1 + -|*\-1 + 7*x / 18*|1 + -| *atan\-1 + 7*x /*cos(9*x) / 3\ 162*cos (9*x)*|1 + -|*atan\-1 + 7*x / 378*x *|1 + -|*cos(9*x) | / / 2\\ |\ \1 + \-1 + 7*x / / / 168 | 14 6174*x 1701*x 1764*x *\-1 + 7*x / 1458*cos (9*x)*atan\-1 + 7*x / 1215*atan\-1 + 7*x /*cos(9*x) 24696*x *\-1 + 7*x / 378*x*cos(9*x) 3402*x *cos (9*x) 7938*x *\-1 + 7*x /*cos(9*x)| / / 2\\ \1 + \-1 + 7*x / / \1 + \-1 + 7*x / / \ x/ \ \ \1 + \-1 + 7*x / / / / \ \1 + \-1 + 7*x / / / 8*atan\-1 + 7*x / \ x/ \ x/ \ x/ \ x/ \ x/ \ x/ 72*atan\-1 + 7*x /*cos(9*x) \ x/ \ x/ | \x + 2*log\5*x // *|--------------------------------------------------------------------------------------------------- - ------------------------------------ + 3*|---------------- - ------------------- + ---------------- - ------------------- - ------------------------------ - ----------------------------- + --------------------- - --------------------------- + ---------------------------- + ----------------------------|*log\x + 2*log\5*x // - -------------------------------------------------- - ---------------------------------------------------------- + -------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------ + -------------------- + -------------------------- - ------------------------------------- + -------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------ + ----------------------------- + ------------------------------------- - ---------------------------------------------| | 2 / 2\ | 2 2 2 2 3 sin(9*x) 3 / 2\ / 2\ 2 | 2 / / 2\\ 2 3 sin(9*x) / 2\ 3 / / 2\\ / 2\ / 2\ 2 2 / 2\ 2 2 2 / / 2\\ / / 2\\ 2 / 2\ | | sin (9*x) | / 3\ | / / 2\\ | / 3\ / 2\ / 3\ / 2\ sin (9*x) / 2\ | / 3\ | | / 3\ | 2 / 2\ | x *\x + 2*log\5*x // / / 2\\ / / 2\\ x + 2*log\5*x / x *\x + 2*log\5*x // x + 2*log\5*x / | / 3\ | / / 2\\ 2 / / 2\\ | / 3\ | / / 2\\ / 2\ / / 2\\ x *\x + 2*log\5*x //*sin(9*x) \x + 2*log\5*x //*sin (9*x) | / 3\ | / / 2\\ | | \1 + \-1 + 7*x / /*\x + 2*log\5*x // |1 + \-1 + 7*x / | / 3\ | 1 + \-1 + 7*x / | / 3\ | | / 3\ | \1 + \-1 + 7*x / /*sin(9*x) \1 + \-1 + 7*x / /*sin (9*x) | / 3\ | | \x + 2*log\5*x // \x + 2*log\5*x // \1 + \-1 + 7*x / /*\x + 2*log\5*x // x *\x + 2*log\5*x // \1 + \-1 + 7*x / /*\x + 2*log\5*x // | / 3\ | / / 2\\ \x + 2*log\5*x // *sin(9*x) \1 + \-1 + 7*x / /*\x + 2*log\5*x //*sin(9*x)| \ \ \1 + \-1 + 7*x / / \1 + \-1 + 7*x / / \1 + \-1 + 7*x / / \1 + \-1 + 7*x / / *sin(9*x)/ \1 + \-1 + 7*x / / *\x + 2*log\5*x // / ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- sin(9*x)