- Решение пределов lim x→∞
- Производная функции f(x)'
- Решение интегралов ∫dx
- Решение уравнений x^2=1
- Система уравнений {x-2y=0}
- Построение графиков f(x)
- Решение неравенств x<1
- Комплексные числа ⅈ
- Ряды ∑
- Матрицы [⊹]
- Вектора
- Обычный и инженерный калькулятор
Как пользоваться?
- Производная:
- x^3
- x
- 3*x
- asin(x)
Идентичные выражения
- (cot(x)^ семь)^atan(sqrt(x))
- ( котангенс от ( х ) в степени 7) в степени арктангенс от ( квадратный корень из ( х ))
- ( котангенс от ( х ) в степени семь) в степени арктангенс от ( квадратный корень из ( х ))
- (cot(x)7)atan(sqrt(x))
- (cot(x)⁷)^atan(sqrt(x))
Похожие выражения
- (ctg(x)^7)^arctg(sqrt(x))
- (ctgx^7)^atan(sqrt(x))
Выражения c функциями
- Котангенс ctg
- cot(x)^(2)
- sqrt(acot(x))
- e^x*cot(x)
- 1/cot(x)
- cot(x/3)
- Арктангенс arctg
- atan(4*x)
- atan(1)/x
- log(atan(x))
- x^2*atan(x)
- atan(sqrt(3*x-1))
- Квадратный корень sqrt
- log(x+sqrt(x^2+1))
- log(x)/sqrt(x)
- sqrt(acot(x))
- sqrt(x)^3
- sqrt(1+2*x)
Топ
- (e^(x^2)-2)'
- (6*sin(3*x))'
- ((sin(x)^2)*(1/3))'
- (f*(x)*3/x^2,((13/10)))'
- (3^(1/(log((5),(x+1)))))'
- (sqrt(2)*(log(x)))'
- (log(sqrt(3*x+1))/log((1/2)))'
- (11+24*x+2*x*sqrt(x))'
- (e^(2-x)*cos((pi*x)/2))'
- ((sqrt(1+x^3)/(1-x^3)))'
- (e^x*sin(t)+e^x*cos(x))'
- (sqrt(x)/(1+sqrt(x)))'
- ((x^7+2*x^5+4)/(x^2-1))'
- (sin(2)^(5)*x+cos(2*x)^5)'
- ((1/2)*cos(3*x-pi/6))'
- (sqrt(2+e^(4*x))^(1/4)+sqrt(3))'
- (3*t^2-e^(3*t)+1)'
- (cos(x)^(315))'
- (k^x)'
- (z^2*sin(1/z))'
- (x^3/(x+2)^3)'
- ((5/11)/(1+(5/11)*t^2))'
- (15+48*x-x^3)'
- (4*sin(pi*t/6))'
- (x*exp(x^(1/8)))'
- (sqrt((cos(x))*sqrt(cos(x))))'
- (6*sin(x)-9*x+5)'
- ((8*x)/(1-4*x^2)^2)'
- (-x^2+20*x-19*x)'
- (-sin(pi*t^2)+1)'
- (ctg^4*(log(2+5*x)/log(3)))'
- (tan(3*x)+pi)'
- (4/(2-e^y))'
- (2*sqrt(x)-4*cos(x)+2*sin(x)+(log(3)/log(x))-log(5))'
- (3-(1/2)*sin(60*t)^(2))'
- ((2+log(x))^sin(x))'
- (-(5/2)/pi^2*sin(2*pi)*t)'
- (20*x+x*(sqrt(400)-sqrt(x)^2))'
- (2*x/(x^2+8))'
- (log(0))'
- (lg3*(x^2-(1-x^2)^(1/2)))'
- (sin(tan(1/7))*(cos(16*x))^2/(32*sin(32*x)))'
- (sin(sqrt(x)/(1+n^2*x))^2)'
- (sqrt(n^2+1))'
- (1/27*((sin(27*x)^(2))/cos(54*x)))'
- (4^(1-x))'
- (e^(2*x)-8*e^x+9)'
- (2^(sqrt((sin(x)^2)*x)))'
- (10^sqrt(x))'
- (x^2+441)'
- (4*sin(5*x^2))'
- (x^cosh(x))'
- (8*x^5+2*cos(x))'
- ((-x)/(x^2-196))'
- (sqrt(5-4*x))'
- (1/3*x^(-3)+1/2*log(4*x))'
- ((sqrt(x^2+1))+(sqrt(x^3+1)^(1/3)))'
- (((e^(z-1)-1)/(z*(z+1)^3*(z-1))))'
- (x*(2500)/x)'
- (3*cos(pi*t/8)^(2)+3)'
- (e^x)'
- (sin(x)*(3*x^9-1))'
- (x^(2)*e^x)'
- (acos(t)^(3))'
- (log(5)^x)'
- (tan(x)*e^(3*x))'
- ((cos(9*x))/(9+cos(9*x)))'
- (-3*x*sqrt(3))'
- (e^x*(1-e^(-x)/x^2))'
Производная (cot(x)^7)^atan(sqrt(x))
Учитель очень удивится увидев твоё верное решение производной 😉
Решение
Вы ввели
[src]
/ ___\
atan\\/ x /
7
cot (x)
$$\left(\cot^{7}{\left (x \right )}\right)^{\operatorname{atan}{\left (\sqrt{x} \right )}}$$
Подробное решение
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
График
Первая производная
[src]
/ ___\
atan\\/ x / // 2 \ / ___\ / 7 \ \
7 |\-7 - 7*cot (x)/*atan\\/ x / log\cot (x)/ |
cot (x) *|---------------------------- + ---------------|
| cot(x) ___ |
\ 2*\/ x *(1 + x)/
$$\left(\frac{\operatorname{atan}{\left (\sqrt{x} \right )}}{\cot{\left (x \right )}} \left(- 7 \cot^{2}{\left (x \right )} - 7\right) + \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{2 \sqrt{x} \left(x + 1\right)}\right) \left(\cot^{7}{\left (x \right )}\right)^{\operatorname{atan}{\left (\sqrt{x} \right )}}$$
Вторая производная
[src]
/ 2 \
|/ / 7 \ / 2 \ / ___\\ |
|| log\cot (x)/ 14*\1 + cot (x)/*atan\\/ x /| |
/ ___\ ||- ------------- + ----------------------------| 2 |
atan\\/ x / || ___ cot(x) | / 2 \ / ___\ / 7 \ / 7 \ / 2 \ |
7 |\ \/ x *(1 + x) / / 2 \ / ___\ 7*\1 + cot (x)/ *atan\\/ x / log\cot (x)/ log\cot (x)/ 7*\1 + cot (x)/ |
cot (x) *|------------------------------------------------- + 14*\1 + cot (x)/*atan\\/ x / - ---------------------------- - ---------------- - -------------- - --------------------|
| 4 2 ___ 2 3/2 ___ |
\ cot (x) 2*\/ x *(1 + x) 4*x *(1 + x) \/ x *(1 + x)*cot(x)/
$$\left(\frac{1}{4} \left(\frac{14 \operatorname{atan}{\left (\sqrt{x} \right )}}{\cot{\left (x \right )}} \left(\cot^{2}{\left (x \right )} + 1\right) - \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{\sqrt{x} \left(x + 1\right)}\right)^{2} - \frac{7 \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{\cot^{2}{\left (x \right )}} \operatorname{atan}{\left (\sqrt{x} \right )} + 14 \left(\cot^{2}{\left (x \right )} + 1\right) \operatorname{atan}{\left (\sqrt{x} \right )} - \frac{7 \cot^{2}{\left (x \right )} + 7}{\sqrt{x} \left(x + 1\right) \cot{\left (x \right )}} - \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{2 \sqrt{x} \left(x + 1\right)^{2}} - \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{4 x^{\frac{3}{2}} \left(x + 1\right)}\right) \left(\cot^{7}{\left (x \right )}\right)^{\operatorname{atan}{\left (\sqrt{x} \right )}}$$
Третья производная
[src]
/ 3 / 2 \ \
| / / 7 \ / 2 \ / ___\\ / / 7 \ / 2 \ / ___\\ | / 7 \ / 7 \ / 2 \ / ___\ / 2 \ | |
| | log\cot (x)/ 14*\1 + cot (x)/*atan\\/ x /| | log\cot (x)/ 14*\1 + cot (x)/*atan\\/ x /| | / 2 \ / ___\ log\cot (x)/ 2*log\cot (x)/ 28*\1 + cot (x)/ *atan\\/ x / 28*\1 + cot (x)/ | |
/ ___\ | |- ------------- + ----------------------------| 3*|- ------------- + ----------------------------|*|- 56*\1 + cot (x)/*atan\\/ x / + ------------ + -------------- + ----------------------------- + --------------------| 3 2 2 |
atan\\/ x / | | ___ cot(x) | | ___ cot(x) | | 3/2 ___ 2 2 ___ | / 7 \ / 7 \ / 2 \ / ___\ / 2 \ / 2 \ / ___\ / 7 \ / 2 \ / 2 \ / 2 \ |
7 | \ \/ x *(1 + x) / \ \/ x *(1 + x) / \ x *(1 + x) \/ x *(1 + x) cot (x) \/ x *(1 + x)*cot(x)/ log\cot (x)/ log\cot (x)/ / 2 \ / ___\ 14*\1 + cot (x)/ *atan\\/ x / 21*\1 + cot (x)/ 28*\1 + cot (x)/ *atan\\/ x / 3*log\cot (x)/ 21*\1 + cot (x)/ 21*\1 + cot (x)/ 21*\1 + cot (x)/ |
cot (x) *|- ------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------- + --------------- - 28*\1 + cot (x)/*atan\\/ x /*cot(x) - ----------------------------- + ---------------- + ----------------------------- + -------------- - ----------------------- + ----------------------- + ---------------------|
| 8 8 ___ 3 3/2 2 3 ___ cot(x) 5/2 ___ 2 ___ 2 3/2 |
\ \/ x *(1 + x) 2*x *(1 + x) cot (x) \/ x *(1 + x) 8*x *(1 + x) 2*\/ x *(1 + x)*cot (x) 2*\/ x *(1 + x) *cot(x) 4*x *(1 + x)*cot(x)/
$$\left(- \frac{1}{8} \left(\frac{14 \operatorname{atan}{\left (\sqrt{x} \right )}}{\cot{\left (x \right )}} \left(\cot^{2}{\left (x \right )} + 1\right) - \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{\sqrt{x} \left(x + 1\right)}\right)^{3} + \frac{3}{8} \left(\frac{14 \operatorname{atan}{\left (\sqrt{x} \right )}}{\cot{\left (x \right )}} \left(\cot^{2}{\left (x \right )} + 1\right) - \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{\sqrt{x} \left(x + 1\right)}\right) \left(\frac{28 \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{\cot^{2}{\left (x \right )}} \operatorname{atan}{\left (\sqrt{x} \right )} - 56 \left(\cot^{2}{\left (x \right )} + 1\right) \operatorname{atan}{\left (\sqrt{x} \right )} + \frac{28 \cot^{2}{\left (x \right )} + 28}{\sqrt{x} \left(x + 1\right) \cot{\left (x \right )}} + \frac{2 \log{\left (\cot^{7}{\left (x \right )} \right )}}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{x^{\frac{3}{2}} \left(x + 1\right)}\right) - \frac{14 \left(\cot^{2}{\left (x \right )} + 1\right)^{3}}{\cot^{3}{\left (x \right )}} \operatorname{atan}{\left (\sqrt{x} \right )} + \frac{28 \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{\cot{\left (x \right )}} \operatorname{atan}{\left (\sqrt{x} \right )} - 28 \left(\cot^{2}{\left (x \right )} + 1\right) \cot{\left (x \right )} \operatorname{atan}{\left (\sqrt{x} \right )} - \frac{21 \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{2 \sqrt{x} \left(x + 1\right) \cot^{2}{\left (x \right )}} + \frac{21 \cot^{2}{\left (x \right )} + 21}{\sqrt{x} \left(x + 1\right)} + \frac{21 \cot^{2}{\left (x \right )} + 21}{2 \sqrt{x} \left(x + 1\right)^{2} \cot{\left (x \right )}} + \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{\sqrt{x} \left(x + 1\right)^{3}} + \frac{21 \cot^{2}{\left (x \right )} + 21}{4 x^{\frac{3}{2}} \left(x + 1\right) \cot{\left (x \right )}} + \frac{\log{\left (\cot^{7}{\left (x \right )} \right )}}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2}} + \frac{3 \log{\left (\cot^{7}{\left (x \right )} \right )}}{8 x^{\frac{5}{2}} \left(x + 1\right)}\right) \left(\cot^{7}{\left (x \right )}\right)^{\operatorname{atan}{\left (\sqrt{x} \right )}}$$
График