Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de -5*tan(2*t)-4*cot(4*t)
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Derivada de (3*sqrt(v)-2*v*e^v)/v
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Derivada de 3^(x*x)
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Derivada de 2*x-8/x
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Expresiones idénticas
- x*sin(x/ tres)*sin(x+ cinco)*cos(x- seis)*sin(x+ siete)*cos(x- ocho)
- x multiplicar por seno de (x dividir por 3) multiplicar por seno de (x más 5) multiplicar por coseno de (x menos 6) multiplicar por seno de (x más 7) multiplicar por coseno de (x menos 8)
- x multiplicar por seno de (x dividir por tres) multiplicar por seno de (x más cinco) multiplicar por coseno de (x menos seis) multiplicar por seno de (x más siete) multiplicar por coseno de (x menos ocho)
- xsin(x/3)sin(x+5)cos(x-6)sin(x+7)cos(x-8)
- xsinx/3sinx+5cosx-6sinx+7cosx-8
- x*sin(x dividir por 3)*sin(x+5)*cos(x-6)*sin(x+7)*cos(x-8)
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Expresiones semejantes
- x*sin(x/3)*sin(x-5)*cos(x-6)*sin(x+7)*cos(x-8)
- x*sin(x/3)*sin(x+5)*cos(x+6)*sin(x+7)*cos(x-8)
- x*sin(x/3)*sin(x+5)*cos(x-6)*sin(x+7)*cos(x+8)
- x*sin(x/3)*sin(x+5)*cos(x-6)*sin(x-7)*cos(x-8)
Derivada de x*sin(x/3)*sin(x+5)*cos(x-6)*sin(x+7)*cos(x-8)
Solución
Ha introducido
[src]
/x\
x*sin|-|*sin(x + 5)*cos(x - 6)*sin(x + 7)*cos(x - 8)
\3/
$$x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 8 \right)}$$
((((x*sin(x/3))*sin(x + 5))*cos(x - 6))*sin(x + 7))*cos(x - 8)
Primera derivada
[src]
//// /x\ \ \ \ \ ||||x*cos|-| | | | | |||| \3/ /x\| /x\| /x\ | /x\ | /x\ ||||-------- + sin|-||*sin(x + 5) + x*cos(x + 5)*sin|-||*cos(x - 6) - x*sin|-|*sin(x - 6)*sin(x + 5)|*sin(x + 7) + x*cos(x - 6)*cos(x + 7)*sin|-|*sin(x + 5)|*cos(x - 8) - x*cos(x - 6)*sin|-|*sin(x - 8)*sin(x + 5)*sin(x + 7) \\\\ 3 \3// \3// \3/ / \3/ / \3/
$$- x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 8 \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 6 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \cos{\left(x + 7 \right)} + \left(- x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(\frac{x \cos{\left(\frac{x}{3} \right)}}{3} + \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \cos{\left(x - 8 \right)}$$
Segunda derivada
[src]
///// /x\ /x\\ / /x\ /x\\ /x\ \ // /x\ /x\\ /x\\ /x\ \ / // /x\ /x\\ /x\\ /x\ \ /x\ \ / / // /x\ /x\\ /x\\ /x\ \ /x\ \ \ |||||- 6*cos|-| + x*sin|-||*sin(5 + x) - 6*|3*sin|-| + x*cos|-||*cos(5 + x) + 9*x*sin|-|*sin(5 + x)|*cos(-6 + x) + 6*||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*sin(-6 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)|*sin(7 + x) + 6*|- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*cos(7 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)*sin(7 + x)|*cos(-8 + x) 2*|- |- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*sin(7 + x) + 3*x*cos(-6 + x)*cos(7 + x)*sin|-|*sin(5 + x)|*sin(-8 + x) | |\\\\ \3/ \3// \ \3/ \3// \3/ / \\ \3/ \3// \3// \3/ / \ \\ \3/ \3// \3// \3/ / \3/ / \ \ \\ \3/ \3// \3// \3/ / \3/ / /x\ | -|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + x*cos(-8 + x)*cos(-6 + x)*sin|-|*sin(5 + x)*sin(7 + x)| \ 9 3 \3/ /
$$- (x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 8 \right)} \cos{\left(x - 6 \right)} + \frac{2 \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \cos{\left(x + 7 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \sin{\left(x - 8 \right)}}{3} + \frac{\left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \cos{\left(x + 7 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \sin{\left(x - 6 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} - 6 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \cos{\left(x - 8 \right)}}{9})$$
Tercera derivada
[src]
/ / // /x\ /x\\ / /x\ /x\\ / /x\ /x\\ /x\\ // /x\ /x\\ /x\\ // /x\ /x\\ / /x\ /x\\ /x\ \ /x\ \ / // /x\ /x\\ /x\\ /x\ \ /// /x\ /x\\ / /x\ /x\\ /x\ \ // /x\ /x\\ /x\\ /x\ \ /x\ \ //// /x\ /x\\ / /x\ /x\\ /x\ \ // /x\ /x\\ /x\\ /x\ \ / // /x\ /x\\ /x\\ /x\ \ /x\ \
|- |- ||9*sin|-| + x*cos|-||*sin(5 + x) + 9*|- 6*cos|-| + x*sin|-||*cos(5 + x) + 27*|3*sin|-| + x*cos|-||*sin(5 + x) + 27*x*cos(5 + x)*sin|-||*cos(-6 + x) - 27*||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 9*||- 6*cos|-| + x*sin|-||*sin(5 + x) - 6*|3*sin|-| + x*cos|-||*cos(5 + x) + 9*x*sin|-|*sin(5 + x)|*sin(-6 + x) + 27*x*sin|-|*sin(-6 + x)*sin(5 + x)|*sin(7 + x) - 27*|- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*sin(7 + x) + 9*|||- 6*cos|-| + x*sin|-||*sin(5 + x) - 6*|3*sin|-| + x*cos|-||*cos(5 + x) + 9*x*sin|-|*sin(5 + x)|*cos(-6 + x) + 6*||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*sin(-6 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)|*cos(7 + x) + 27*x*cos(-6 + x)*cos(7 + x)*sin|-|*sin(5 + x)|*cos(-8 + x) ||||- 6*cos|-| + x*sin|-||*sin(5 + x) - 6*|3*sin|-| + x*cos|-||*cos(5 + x) + 9*x*sin|-|*sin(5 + x)|*cos(-6 + x) + 6*||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*sin(-6 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)|*sin(7 + x) + 6*|- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*cos(7 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)*sin(7 + x)|*sin(-8 + x)
/ / // /x\ /x\\ /x\\ /x\ \ /x\ \ \ \ \\ \3/ \3// \ \3/ \3// \ \3/ \3// \3// \\ \3/ \3// \3// \\ \3/ \3// \ \3/ \3// \3/ / \3/ / \ \\ \3/ \3// \3// \3/ / \\\ \3/ \3// \ \3/ \3// \3/ / \\ \3/ \3// \3// \3/ / \3/ / \\\\ \3/ \3// \ \3/ \3// \3/ / \\ \3/ \3// \3// \3/ / \ \\ \3/ \3// \3// \3/ / \3/ / /x\
- |- |- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*sin(7 + x) + 3*x*cos(-6 + x)*cos(7 + x)*sin|-|*sin(5 + x)|*cos(-8 + x) - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + x*cos(-6 + x)*sin|-|*sin(-8 + x)*sin(5 + x)*sin(7 + x)
\ \ \\ \3/ \3// \3// \3/ / \3/ / 27 3 \3/
$$x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 8 \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 6 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \cos{\left(x + 7 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \cos{\left(x - 8 \right)} + \frac{\left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \cos{\left(x + 7 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \sin{\left(x - 6 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} - 6 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \sin{\left(x - 8 \right)}}{3} - \frac{\left(27 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \cos{\left(x + 7 \right)} - 27 \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)} + 9 \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \sin{\left(x - 6 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} - 6 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \cos{\left(x + 7 \right)} - \left(27 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - 27 \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)} + 9 \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} - 6 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)}\right) \sin{\left(x - 6 \right)} - \left(27 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + 9 \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)} + 27 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 9 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \cos{\left(x - 8 \right)}}{27}$$
Gráfico