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 x/4
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Derivada de x^(2*x)
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Derivada de 6
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Derivada de x^(3*x)
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Expresiones idénticas
- log((uno +sqrt(sin(x)))/(uno -sqrt(sin(x))))+ dos *atan(sqrt(sin(x)))
- logaritmo de ((1 más raíz cuadrada de ( seno de (x))) dividir por (1 menos raíz cuadrada de ( seno de (x)))) más 2 multiplicar por arco tangente de gente de ( raíz cuadrada de ( seno de (x)))
- logaritmo de ((uno más raíz cuadrada de ( seno de (x))) dividir por (uno menos raíz cuadrada de ( seno de (x)))) más dos multiplicar por arco tangente de gente de ( raíz cuadrada de ( seno de (x)))
- log((1+√(sin(x)))/(1-√(sin(x))))+2*atan(√(sin(x)))
- log((1+sqrt(sin(x)))/(1-sqrt(sin(x))))+2atan(sqrt(sin(x)))
- log1+sqrtsinx/1-sqrtsinx+2atansqrtsinx
- log((1+sqrt(sin(x))) dividir por (1-sqrt(sin(x))))+2*atan(sqrt(sin(x)))
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Expresiones semejantes
- log((1+sqrt(sin(x)))/(1+sqrt(sin(x))))+2*atan(sqrt(sin(x)))
- log((1+sqrt(sin(x)))/(1-sqrt(sin(x))))-2*atan(sqrt(sin(x)))
- log((1-sqrt(sin(x)))/(1-sqrt(sin(x))))+2*atan(sqrt(sin(x)))
- log((1+sqrt(sin(x)))/(1-sqrt(sin(x))))+2*arctan(sqrt(sin(x)))
- log((1+sqrt(sinx))/(1-sqrt(sinx)))+2*atan(sqrt(sinx))
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Expresiones con funciones
- Logaritmo log
- log(1-x^2)
- log(x)/sqrt(x)
- log(tan(2*x))
- log((1+x)/(1-x))
- log(x^2*e^x)
- Raíz cuadrada sqrt
- sqrt
- sqrt3x
- sqrt(3*x)
- sqrt(x)^2
- sqrt(x^2-3)
- Seno sin
- sin(x)^(3)
- sin(2*x+3)
- sin^3*x
- sin^2*x
- sin(3-x)
- Raíz cuadrada sqrt
- sqrt
- sqrt3x
- sqrt(3*x)
- sqrt(x)^2
- sqrt(x^2-3)
- Seno sin
- sin(x)^(3)
- sin(2*x+3)
- sin^3*x
- sin^2*x
- sin(3-x)
- Arcotangente arctan
- atan(x)*sqrt(x^2-1)
- atan(x/2)
- atan(x/3)
- atan(x-(sqrt(1+x^2)))
- atan(2*x+3)
- Raíz cuadrada sqrt
- sqrt
- sqrt3x
- sqrt(3*x)
- sqrt(x)^2
- sqrt(x^2-3)
- Seno sin
- sin(x)^(3)
- sin(2*x+3)
- sin^3*x
- sin^2*x
- sin(3-x)
Derivada de log((1+sqrt(sin(x)))/(1-sqrt(sin(x))))+2*atan(sqrt(sin(x)))
Solución
Ha introducido
[src]
/ ________\ |1 + \/ sin(x) | / ________\ log|--------------| + 2*atan\\/ sin(x) / | ________| \1 - \/ sin(x) /
$$\log{\left(\frac{\sqrt{\sin{\left(x \right)}} + 1}{1 - \sqrt{\sin{\left(x \right)}}} \right)} + 2 \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)}$$
log((1 + sqrt(sin(x)))/(1 - sqrt(sin(x)))) + 2*atan(sqrt(sin(x)))
Primera derivada
[src]
/ / ________\ \
/ ________\ | cos(x) \1 + \/ sin(x) /*cos(x) |
\1 - \/ sin(x) /*|----------------------------- + ------------------------------|
| / ________\ ________ 2 |
|2*\1 - \/ sin(x) /*\/ sin(x) / ________\ ________|
\ 2*\1 - \/ sin(x) / *\/ sin(x) / cos(x)
--------------------------------------------------------------------------------- + -----------------------
________ ________
1 + \/ sin(x) (1 + sin(x))*\/ sin(x)
$$\frac{\left(1 - \sqrt{\sin{\left(x \right)}}\right) \left(\frac{\cos{\left(x \right)}}{2 \left(1 - \sqrt{\sin{\left(x \right)}}\right) \sqrt{\sin{\left(x \right)}}} + \frac{\left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos{\left(x \right)}}{2 \left(1 - \sqrt{\sin{\left(x \right)}}\right)^{2} \sqrt{\sin{\left(x \right)}}}\right)}{\sqrt{\sin{\left(x \right)}} + 1} + \frac{\cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}}}$$
Segunda derivada
[src]
2 ________ / ________\ 2 2 / ________\ 2 / ________\
________ cos (x) 2*\/ sin(x) *\1 + \/ sin(x) / 2*cos (x) cos (x)*\1 + \/ sin(x) / 2*cos (x)*\1 + \/ sin(x) / / ________\ / ________\
2*\/ sin(x) + --------- - ----------------------------- + ------------------------ - --------------------------- - -------------------------- 2 | 1 + \/ sin(x) | 2 | 1 + \/ sin(x) |
3/2 ________ / ________\ / ________\ 3/2 2 cos (x)*|1 - ---------------| cos (x)*|1 - ---------------|
________ sin (x) -1 + \/ sin(x) \-1 + \/ sin(x) /*sin(x) \-1 + \/ sin(x) /*sin (x) / ________\ 2 2 | ________| | ________|
\/ sin(x) \-1 + \/ sin(x) / *sin(x) cos (x) cos (x) \ -1 + \/ sin(x) / \ -1 + \/ sin(x) /
- ---------- - ---------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------ - ------------------------ - ----------------------------- + -------------------------------------------
1 + sin(x) / ________\ 2 ________ 3/2 2 / ________\ / ________\
4*\1 + \/ sin(x) / (1 + sin(x)) *\/ sin(x) 2*(1 + sin(x))*sin (x) / ________\ 4*\1 + \/ sin(x) /*\-1 + \/ sin(x) /*sin(x)
4*\1 + \/ sin(x) / *sin(x)
$$- \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2} \sin{\left(x \right)}} + \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{4 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sin{\left(x \right)}} - \frac{\sqrt{\sin{\left(x \right)}}}{\sin{\left(x \right)} + 1} - \frac{\cos^{2}{\left(x \right)}}{2 \left(\sin{\left(x \right)} + 1\right) \sin^{\frac{3}{2}}{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{2} \sqrt{\sin{\left(x \right)}}} - \frac{2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sqrt{\sin{\left(x \right)}}}{\sqrt{\sin{\left(x \right)}} - 1} - \frac{\left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin{\left(x \right)}}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)}$$
Tercera derivada
[src]
/ / ________\ 2 / ________\ 2 2 2 / ________\ 2 / ________\ 2 / ________\ 2 ________ / ________\ 2 2 / ________\ 2 / ________\ 2 ________ / ________\ 2 2 / ________\ 2 / ________\ \ | ________ 2 12 12*\1 + \/ sin(x) / 3*cos (x) 2*\1 + \/ sin(x) / 6*cos (x) 6*cos (x) 6*cos (x)*\1 + \/ sin(x) / 6*cos (x)*\1 + \/ sin(x) / 3*cos (x)*\1 + \/ sin(x) / ________ ________ cos (x) 2*\/ sin(x) *\1 + \/ sin(x) / 2*cos (x) cos (x)*\1 + \/ sin(x) / 2*cos (x)*\1 + \/ sin(x) / ________ cos (x) 2*\/ sin(x) *\1 + \/ sin(x) / 2*cos (x) cos (x)*\1 + \/ sin(x) / 2*cos (x)*\1 + \/ sin(x) / / ________\ / ________\ / ________\ / ________\ | | 1 + \/ sin(x) ---------- + --------------- - ------------------- + --------- - ---------------------------- + ------------------------- + ---------------------------- - ---------------------------- - -------------------------- - --------------------------- 1 + \/ sin(x) 2*\/ sin(x) + --------- - ----------------------------- + ------------------------ - --------------------------- - -------------------------- 2*\/ sin(x) + --------- - ----------------------------- + ------------------------ - --------------------------- - -------------------------- 2 | 1 + \/ sin(x) | 2 | 1 + \/ sin(x) | 2 | 1 + \/ sin(x) | 2 | 1 + \/ sin(x) | | | 1 - --------------- ________ ________ 2 5/2 / ________\ ________ / ________\ 2 2 3 2 / ________\ 5/2 1 - --------------- 3/2 ________ / ________\ / ________\ 3/2 2 3/2 ________ / ________\ / ________\ 3/2 2 cos (x)*|1 - ---------------| cos (x)*|1 - ---------------| cos (x)*|1 - ---------------| cos (x)*|1 - ---------------| | | ________ ________ \/ sin(x) -1 + \/ sin(x) / ________\ sin (x) \-1 + \/ sin(x) /*\/ sin(x) \-1 + \/ sin(x) /*sin (x) / ________\ 3/2 / ________\ 3/2 / ________\ 2 \-1 + \/ sin(x) /*sin (x) 2 2 ________ sin (x) -1 + \/ sin(x) \-1 + \/ sin(x) /*sin(x) \-1 + \/ sin(x) /*sin (x) / ________\ 2 sin (x) -1 + \/ sin(x) \-1 + \/ sin(x) /*sin(x) \-1 + \/ sin(x) /*sin (x) / ________\ | ________| | ________| | ________| | ________| | | 1 3*\/ sin(x) -1 + \/ sin(x) \-1 + \/ sin(x) / \-1 + \/ sin(x) / *sin (x) \-1 + \/ sin(x) / *sin (x) \-1 + \/ sin(x) / *sin (x) cos (x) 2*cos (x) -1 + \/ sin(x) \-1 + \/ sin(x) / *sin(x) 3*cos (x) \-1 + \/ sin(x) / *sin(x) \ -1 + \/ sin(x) / \ -1 + \/ sin(x) / \ -1 + \/ sin(x) / \ -1 + \/ sin(x) / | |------------------------- + ------------- + ------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------- + ------------------------ - ------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------- + ----------------------------- - ----------------------------------------------- - --------------------------------------------|*cos(x) | ________ 2 2 / ________\ 2 3/2 3 ________ / ________\ / ________\ 2 5/2 / ________\ / ________\ ________ 3 2 2 / ________\ / ________\ 2 | |2*(1 + sin(x))*\/ sin(x) (1 + sin(x)) / ________\ 8*\1 + \/ sin(x) / (1 + sin(x)) *sin (x) (1 + sin(x)) *\/ sin(x) 4*\1 + \/ sin(x) /*\-1 + \/ sin(x) / / ________\ ________ 4*(1 + sin(x))*sin (x) 4*\1 + \/ sin(x) /*\-1 + \/ sin(x) /*\/ sin(x) / ________\ 3/2 / ________\ 2 / ________\ / ________\ 3/2 8*\1 + \/ sin(x) /*\-1 + \/ sin(x) /*sin (x)| \ 4*\1 + \/ sin(x) / 4*\1 + \/ sin(x) / *\/ sin(x) 4*\1 + \/ sin(x) / *sin (x) 8*\1 + \/ sin(x) / *sin (x) 4*\1 + \/ sin(x) / *\-1 + \/ sin(x) /*sin (x) /
$$\left(\frac{1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2}} + \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{8 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2} \sin^{2}{\left(x \right)}} + \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{3} \sin^{\frac{3}{2}}{\left(x \right)}} - \frac{1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}}{4 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right)} - \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{8 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sin^{2}{\left(x \right)}} - \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{4 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2} \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{1}{2 \left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}}} + \frac{3 \cos^{2}{\left(x \right)}}{4 \left(\sin{\left(x \right)} + 1\right) \sin^{\frac{5}{2}}{\left(x \right)}} + \frac{3 \sqrt{\sin{\left(x \right)}}}{\left(\sin{\left(x \right)} + 1\right)^{2}} + \frac{\cos^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{2} \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \cos^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{3} \sqrt{\sin{\left(x \right)}}} + \frac{\frac{2}{\sqrt{\sin{\left(x \right)}}} + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{\frac{5}{2}}{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right)}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sqrt{\sin{\left(x \right)}}} - \frac{3 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{\frac{5}{2}}{\left(x \right)}} + \frac{12}{\sqrt{\sin{\left(x \right)}} - 1} + \frac{6 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{2}{\left(x \right)}} - \frac{12 \left(\sqrt{\sin{\left(x \right)}} + 1\right)}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2}} - \frac{6 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin^{2}{\left(x \right)}} + \frac{6 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin^{\frac{3}{2}}{\left(x \right)}} - \frac{6 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{3} \sin^{\frac{3}{2}}{\left(x \right)}}}{8 \left(\sqrt{\sin{\left(x \right)}} + 1\right)} + \frac{2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sqrt{\sin{\left(x \right)}}}{\sqrt{\sin{\left(x \right)}} - 1} - \frac{\left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin{\left(x \right)}}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2} \sqrt{\sin{\left(x \right)}}} - \frac{2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sqrt{\sin{\left(x \right)}}}{\sqrt{\sin{\left(x \right)}} - 1} - \frac{\left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin{\left(x \right)}}}{4 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sqrt{\sin{\left(x \right)}}}\right) \cos{\left(x \right)}$$
Gráfico