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:
-
Derivada de v
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Derivada de (x+12)e^(12-x)
- Derivada de u/v
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Derivada de x^(1/10)
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Expresiones idénticas
- y=arccos((uno -sqrt(x))/(uno +sqrt(x)))^ dos
- y es igual a arc coseno de ((1 menos raíz cuadrada de (x)) dividir por (1 más raíz cuadrada de (x))) al cuadrado
- y es igual a arc coseno de ((uno menos raíz cuadrada de (x)) dividir por (uno más raíz cuadrada de (x))) en el grado dos
- y=arccos((1-√(x))/(1+√(x)))^2
- y=arccos((1-sqrt(x))/(1+sqrt(x)))2
- y=arccos1-sqrtx/1+sqrtx2
- y=arccos((1-sqrt(x))/(1+sqrt(x)))²
- y=arccos((1-sqrt(x))/(1+sqrt(x))) en el grado 2
- y=arccos1-sqrtx/1+sqrtx^2
- y=arccos((1-sqrt(x)) dividir por (1+sqrt(x)))^2
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Expresiones semejantes
- y=arccos((1-sqrt(x))/(1-sqrt(x)))^2
- y=arccos((1+sqrt(x))/(1+sqrt(x)))^2
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(10*x)
- Raíz cuadrada sqrt
- sqrt(10*x)
Derivada de y=arccos((1-sqrt(x))/(1+sqrt(x)))^2
Solución
Ha introducido
[src]
/ ___\
2|1 - \/ x |
acos |---------|
| ___|
\1 + \/ x /
$$\operatorname{acos}^{2}{\left(\frac{1 - \sqrt{x}}{\sqrt{x} + 1} \right)}$$
acos((1 - sqrt(x))/(1 + sqrt(x)))^2
Primera derivada
[src]
/ ___ \ / ___\
| 1 1 - \/ x | |1 - \/ x |
-2*|- ------------------- - --------------------|*acos|---------|
| ___ / ___\ 2| | ___|
| 2*\/ x *\1 + \/ x / ___ / ___\ | \1 + \/ x /
\ 2*\/ x *\1 + \/ x / /
-----------------------------------------------------------------
__________________
/ 2
/ / ___\
/ \1 - \/ x /
/ 1 - ------------
/ 2
/ / ___\
\/ \1 + \/ x /
$$- \frac{2 \left(- \frac{1 - \sqrt{x}}{2 \sqrt{x} \left(\sqrt{x} + 1\right)^{2}} - \frac{1}{2 \sqrt{x} \left(\sqrt{x} + 1\right)}\right) \operatorname{acos}{\left(\frac{1 - \sqrt{x}}{\sqrt{x} + 1} \right)}}{\sqrt{- \frac{\left(1 - \sqrt{x}\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} + 1}}$$
Segunda derivada
[src]
/ ___ / ___\\ / / ___\ \ 2 2
| 1 2 -1 + \/ x 2*\-1 + \/ x /| |-\-1 + \/ x / | / ___\ / ___\ / / ___\ \
|- ---- - ------------- + ---------------- + --------------|*acos|--------------| | -1 + \/ x | | -1 + \/ x | / ___\ |-\-1 + \/ x / |
| 3/2 / ___\ 3/2 / ___\ 2| | ___ | |-1 + ----------| |-1 + ----------| *\-1 + \/ x /*acos|--------------|
| x x*\1 + \/ x / x *\1 + \/ x / / ___\ | \ 1 + \/ x / | ___ | | ___ | | ___ |
\ x*\1 + \/ x / / \ 1 + \/ x / \ 1 + \/ x / \ 1 + \/ x /
--------------------------------------------------------------------------------- - ---------------------------------- + ----------------------------------------------------
__________________ / 2\ 3/2
/ 2 | / ___\ | / 2\
/ / ___\ / ___\ | \-1 + \/ x / | 2 | / ___\ |
/ \1 - \/ x / x*\1 + \/ x /*|-1 + -------------| / ___\ | \1 - \/ x / |
/ 1 - ------------ | 2| x*\1 + \/ x / *|1 - ------------|
/ 2 | / ___\ | | 2|
/ / ___\ \ \1 + \/ x / / | / ___\ |
\/ \1 + \/ x / \ \1 + \/ x / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ___\
2*\1 + \/ x /
$$\frac{\frac{\left(\frac{2 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{\sqrt{x} - 1}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{acos}{\left(- \frac{\sqrt{x} - 1}{\sqrt{x} + 1} \right)}}{\sqrt{- \frac{\left(1 - \sqrt{x}\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} + 1}} + \frac{\left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{2} \operatorname{acos}{\left(- \frac{\sqrt{x} - 1}{\sqrt{x} + 1} \right)}}{x \left(\sqrt{x} + 1\right)^{2} \left(- \frac{\left(1 - \sqrt{x}\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} + 1\right)^{\frac{3}{2}}} - \frac{\left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{2}}{x \left(\sqrt{x} + 1\right) \left(\frac{\left(\sqrt{x} - 1\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} - 1\right)}}{2 \left(\sqrt{x} + 1\right)}$$
Tercera derivada
[src]
/ 2 2\
/ ___ / ___\ / ___\ \ / / ___\ \ 3 / ___\ / ___ / ___\\ / ___\ | ___ / ___\ / ___\ / ___\ | / / ___\ \ 3 / ___\ / ___ / ___\\ / / ___\ \
| 1 2 2 -1 + \/ x 2*\-1 + \/ x / 2*\-1 + \/ x / | |-\-1 + \/ x / | / ___\ | -1 + \/ x | | 1 2 -1 + \/ x 2*\-1 + \/ x /| | -1 + \/ x | |1 -1 + \/ x \-1 + \/ x / 4*\-1 + \/ x / 3*\-1 + \/ x / | |-\-1 + \/ x / | 2 / ___\ / / ___\ \ / ___\ | -1 + \/ x | | 1 2 -1 + \/ x 2*\-1 + \/ x /| |-\-1 + \/ x / |
3*|- ---- - -------------- - ----------------- + ---------------- + --------------- + -----------------|*acos|--------------| | -1 + \/ x | / ___\ 3*|-1 + ----------|*|- ---- - ------------- + ---------------- + --------------| |-1 + ----------|*|- - ---------- + ---------------- - -------------- + ---------------|*acos|--------------| / ___\ | -1 + \/ x | |-\-1 + \/ x / | 2*\-1 + \/ x /*|-1 + ----------|*|- ---- - ------------- + ---------------- + --------------|*acos|--------------|
| 5/2 2 / ___\ 2 5/2 / ___\ 2 3| | ___ | 3*|-1 + ----------| *\-1 + \/ x / | ___ | | 3/2 / ___\ 3/2 / ___\ 2| | ___ | |x 3/2 3/2 / ___\ / ___\ 2| | ___ | 3*\-1 + \/ x / *|-1 + ----------| *acos|--------------| | ___ | | 3/2 / ___\ 3/2 / ___\ 2| | ___ |
| x x *\1 + \/ x / 3/2 / ___\ x *\1 + \/ x / 2 / ___\ 3/2 / ___\ | \ 1 + \/ x / | ___ | \ 1 + \/ x / | x x*\1 + \/ x / x *\1 + \/ x / / ___\ | \ 1 + \/ x / | x x *\1 + \/ x / x*\1 + \/ x / / ___\ | \ 1 + \/ x / | ___ | | ___ | \ 1 + \/ x / | x x*\1 + \/ x / x *\1 + \/ x / / ___\ | \ 1 + \/ x /
\ x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / / \ 1 + \/ x / \ x*\1 + \/ x / / \ x*\1 + \/ x / / \ 1 + \/ x / \ 1 + \/ x / \ x*\1 + \/ x / /
- ----------------------------------------------------------------------------------------------------------------------------- - --------------------------------------- + -------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------
__________________ 2 / 2\ 3/2 5/2 3/2
/ 2 / 2\ | / ___\ | / 2\ / 2\ / 2\
/ / ___\ 3 | / ___\ | ___ / ___\ | \-1 + \/ x / | 2 | / ___\ | 4 | / ___\ | 2 | / ___\ |
/ \1 - \/ x / 3/2 / ___\ | \-1 + \/ x / | \/ x *\1 + \/ x /*|-1 + -------------| ___ / ___\ | \1 - \/ x / | 3/2 / ___\ | \1 - \/ x / | ___ / ___\ | \1 - \/ x / |
/ 1 - ------------ x *\1 + \/ x / *|-1 + -------------| | 2| \/ x *\1 + \/ x / *|1 - ------------| x *\1 + \/ x / *|1 - ------------| \/ x *\1 + \/ x / *|1 - ------------|
/ 2 | 2| | / ___\ | | 2| | 2| | 2|
/ / ___\ | / ___\ | \ \1 + \/ x / / | / ___\ | | / ___\ | | / ___\ |
\/ \1 + \/ x / \ \1 + \/ x / / \ \1 + \/ x / / \ \1 + \/ x / / \ \1 + \/ x / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ___\
4*\1 + \/ x /
$$\frac{- \frac{3 \left(\frac{2 \left(\sqrt{x} - 1\right)}{x^{2} \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x^{2} \left(\sqrt{x} + 1\right)} + \frac{2 \left(\sqrt{x} - 1\right)}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{3}} - \frac{2}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{\sqrt{x} - 1}{x^{\frac{5}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{5}{2}}}\right) \operatorname{acos}{\left(- \frac{\sqrt{x} - 1}{\sqrt{x} + 1} \right)}}{\sqrt{- \frac{\left(1 - \sqrt{x}\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} + 1}} - \frac{2 \left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right) \left(\frac{2 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{\sqrt{x} - 1}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{acos}{\left(- \frac{\sqrt{x} - 1}{\sqrt{x} + 1} \right)}}{\sqrt{x} \left(\sqrt{x} + 1\right)^{2} \left(- \frac{\left(1 - \sqrt{x}\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} + 1\right)^{\frac{3}{2}}} + \frac{3 \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right) \left(\frac{2 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{\sqrt{x} - 1}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}\right)}{\sqrt{x} \left(\sqrt{x} + 1\right) \left(\frac{\left(\sqrt{x} - 1\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} - 1\right)} - \frac{\left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right) \left(\frac{3 \left(\sqrt{x} - 1\right)^{2}}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{4 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)} + \frac{1}{x} + \frac{\left(\sqrt{x} - 1\right)^{2}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{\sqrt{x} - 1}{x^{\frac{3}{2}}}\right) \operatorname{acos}{\left(- \frac{\sqrt{x} - 1}{\sqrt{x} + 1} \right)}}{\sqrt{x} \left(\sqrt{x} + 1\right)^{2} \left(- \frac{\left(1 - \sqrt{x}\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} + 1\right)^{\frac{3}{2}}} - \frac{3 \left(\sqrt{x} - 1\right)^{2} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{3} \operatorname{acos}{\left(- \frac{\sqrt{x} - 1}{\sqrt{x} + 1} \right)}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} + 1\right)^{\frac{5}{2}}} - \frac{3 \left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{3}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{3} \left(\frac{\left(\sqrt{x} - 1\right)^{2}}{\left(\sqrt{x} + 1\right)^{2}} - 1\right)^{2}}}{4 \left(\sqrt{x} + 1\right)}$$
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