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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- Derivada de:
-
Derivada de x^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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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)
Derivada de y=arccos(((1-sqrt(x))/(1+sqrt(x)))^2)
Solución
Ha introducido
[src]
/ 2\
|/ ___\ |
||1 - \/ x | |
acos||---------| |
|| ___| |
\\1 + \/ x / /
$$\operatorname{acos}{\left(\left(\frac{1 - \sqrt{x}}{\sqrt{x} + 1}\right)^{2} \right)}$$
acos(((1 - sqrt(x))/(1 + sqrt(x)))^2)
Primera derivada
[src]
/ ___ \
/ ___\ | 1 1 - \/ x |
-\1 - \/ x /*|- ----------------- - ------------------|
| ___ / ___\ 2|
| \/ x *\1 + \/ x / ___ / ___\ |
\ \/ x *\1 + \/ x / /
--------------------------------------------------------
__________________
/ 4
/ / ___\
/ ___\ / \1 - \/ x /
\1 + \/ x /* / 1 - ------------
/ 4
/ / ___\
\/ \1 + \/ x /
$$- \frac{\left(1 - \sqrt{x}\right) \left(- \frac{1 - \sqrt{x}}{\sqrt{x} \left(\sqrt{x} + 1\right)^{2}} - \frac{1}{\sqrt{x} \left(\sqrt{x} + 1\right)}\right)}{\left(\sqrt{x} + 1\right) \sqrt{- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1}}$$
Segunda derivada
[src]
/ ___ / ___\\ 2
___ / ___\ | 1 2 -1 + \/ x 2*\-1 + \/ x /| / ___\ 4 / ___\
-1 + \/ x \-1 + \/ x /*|- ---- - ------------- + ---------------- + --------------| / ___\ | -1 + \/ x | / ___\ | -1 + \/ x |
-1 + ---------- | 3/2 / ___\ 3/2 / ___\ 2| \-1 + \/ x /*|-1 + ----------| \-1 + \/ x / *|-1 + ----------|
___ | x x*\1 + \/ x / x *\1 + \/ x / / ___\ | | ___ | | ___ |
1 + \/ x \ x*\1 + \/ x / / \ 1 + \/ x / \ 1 + \/ x /
--------------- - ------------------------------------------------------------------------- - ------------------------------ - ---------------------------------
2*x 2 / ___\ / 4\
2*x*\1 + \/ x / 4 | / ___\ |
/ ___\ | \1 - \/ x / |
x*\1 + \/ x / *|1 - ------------|
| 4|
| / ___\ |
\ \1 + \/ x / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------
__________________
/ 4
2 / / ___\
/ ___\ / \1 - \/ x /
\1 + \/ x / * / 1 - ------------
/ 4
/ / ___\
\/ \1 + \/ x /
$$\frac{- \frac{\left(\sqrt{x} - 1\right) \left(\frac{2 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{\sqrt{x} - 1}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}\right)}{2} - \frac{\left(\sqrt{x} - 1\right)^{4} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{2}}{x \left(\sqrt{x} + 1\right)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} - \frac{\left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)}{2 x \left(\sqrt{x} + 1\right)} + \frac{\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1}{2 x}}{\left(\sqrt{x} + 1\right)^{2} \sqrt{- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1}}$$
Tercera derivada
[src]
/ 2 2\
___ / ___\ / ___ / ___\ / ___\ \ / ___ / ___\\ 2 2 3 4 / ___\ / ___ / ___\\ 3 / ___\ | ___ / ___\ / ___\ / ___\ |
1 2 -1 + \/ x 2*\-1 + \/ x / ___ / ___\ | 1 2 2 -1 + \/ x 2*\-1 + \/ x / 2*\-1 + \/ x / | ___ / ___\ / ___\ | 1 2 -1 + \/ x 2*\-1 + \/ x /| / ___\ 4 / ___\ 3 / ___\ 7 / ___\ / ___\ | -1 + \/ x | | 1 2 -1 + \/ x 2*\-1 + \/ x /| / ___\ | -1 + \/ x | |3 -1 + \/ x \-1 + \/ x / 8*\-1 + \/ x / 5*\-1 + \/ x / |
- ---- - ------------- + ---------------- + -------------- -1 + \/ x 3*\-1 + \/ x /*|- ---- - -------------- - ----------------- + ---------------- + --------------- + -----------------| -1 + \/ x / ___\ | -1 + \/ x | \-1 + \/ x /*|- ---- - ------------- + ---------------- + --------------| / ___\ | -1 + \/ x | / ___\ | -1 + \/ x | / ___\ | -1 + \/ x | / ___\ | -1 + \/ x | \-1 + \/ x / *|-1 + ----------|*|- ---- - ------------- + ---------------- + --------------| \-1 + \/ x / *|-1 + ----------|*|- - ---------- + ---------------- - -------------- + ---------------|
3/2 / ___\ 3/2 / ___\ 2 -1 + ---------- | 5/2 2 / ___\ 2 5/2 / ___\ 2 3| -1 + ---------- \-1 + \/ x /*|-1 + ----------| | 3/2 / ___\ 3/2 / ___\ 2| \-1 + \/ x /*|-1 + ----------| \-1 + \/ x / *|-1 + ----------| \-1 + \/ x / *|-1 + ----------| 3*\-1 + \/ x / *|-1 + ----------| | ___ | | 3/2 / ___\ 3/2 / ___\ 2| | ___ | |x 3/2 3/2 / ___\ / ___\ 2|
x x*\1 + \/ x / x *\1 + \/ x / / ___\ ___ | x x *\1 + \/ x / 3/2 / ___\ x *\1 + \/ x / 2 / ___\ 3/2 / ___\ | ___ | ___ | | x x*\1 + \/ x / x *\1 + \/ x / / ___\ | | ___ | | ___ | | ___ | | ___ | \ 1 + \/ x / | x x*\1 + \/ x / x *\1 + \/ x / / ___\ | \ 1 + \/ x / | x x *\1 + \/ x / x*\1 + \/ x / / ___\ |
x*\1 + \/ x / 1 + \/ x \ x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / / 1 + \/ x \ 1 + \/ x / \ x*\1 + \/ x / / \ 1 + \/ x / \ 1 + \/ x / \ 1 + \/ x / \ 1 + \/ x / \ x*\1 + \/ x / / \ x*\1 + \/ x / /
- ---------------------------------------------------------- - --------------- + --------------------------------------------------------------------------------------------------------------------- - ------------------ + ------------------------------ + ------------------------------------------------------------------------- + ------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------- + -------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------
___ 2 4 3/2 / ___\ 2 ___ / ___\ 2 / ___\ / 4\ / 4\ 2 / 4\ / 4\
2*\/ x 4*x 2*x *\1 + \/ x / 3/2 / ___\ 2*\/ x *\1 + \/ x / 4*x *\1 + \/ x / 5 | / ___\ | 4 | / ___\ | / 4\ 4 | / ___\ | 4 | / ___\ |
2*x *\1 + \/ x / 3/2 / ___\ | \1 - \/ x / | 3/2 / ___\ | \1 - \/ x / | 8 | / ___\ | ___ / ___\ | \1 - \/ x / | ___ / ___\ | \1 - \/ x / |
x *\1 + \/ x / *|1 - ------------| x *\1 + \/ x / *|1 - ------------| 3/2 / ___\ | \1 - \/ x / | \/ x *\1 + \/ x / *|1 - ------------| 2*\/ x *\1 + \/ x / *|1 - ------------|
| 4| | 4| x *\1 + \/ x / *|1 - ------------| | 4| | 4|
| / ___\ | | / ___\ | | 4| | / ___\ | | / ___\ |
\ \1 + \/ x / / \ \1 + \/ x / / | / ___\ | \ \1 + \/ x / / \ \1 + \/ x / /
\ \1 + \/ x / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
__________________
/ 4
2 / / ___\
/ ___\ / \1 - \/ x /
\1 + \/ x / * / 1 - ------------
/ 4
/ / ___\
\/ \1 + \/ x /
$$\frac{\frac{3 \left(\sqrt{x} - 1\right) \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)}{4} + \frac{\left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)}{4 x^{2} \left(\sqrt{x} + 1\right)} - \frac{\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1}{4 x^{2}} + \frac{\left(\sqrt{x} - 1\right)^{4} \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)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} + \frac{\left(\sqrt{x} - 1\right)^{3} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right) \left(\frac{5 \left(\sqrt{x} - 1\right)^{2}}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{8 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)} + \frac{3}{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)}{2 \sqrt{x} \left(\sqrt{x} + 1\right)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} + \frac{\left(\sqrt{x} - 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)}{2 \sqrt{x} \left(\sqrt{x} + 1\right)} - \frac{\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}}}}{2 \sqrt{x}} + \frac{3 \left(\sqrt{x} - 1\right)^{7} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{3}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{8} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)^{2}} + \frac{\left(\sqrt{x} - 1\right)^{4} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{2}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{5} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} - \frac{\left(\sqrt{x} - 1\right)^{3} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{2}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} + \frac{\left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)}{2 x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2}} - \frac{\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1}{2 x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)}}{\left(\sqrt{x} + 1\right)^{2} \sqrt{- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1}}$$
Gráfico