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^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de (-2)/x^3
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Expresiones idénticas
- x^(sqrt((uno -x)/(uno +x)))
- x en el grado ( raíz cuadrada de ((1 menos x) dividir por (1 más x)))
- x en el grado ( raíz cuadrada de ((uno menos x) dividir por (uno más x)))
- x^(√((1-x)/(1+x)))
- x(sqrt((1-x)/(1+x)))
- xsqrt1-x/1+x
- x^sqrt1-x/1+x
- x^(sqrt((1-x) dividir por (1+x)))
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Expresiones semejantes
- x^(sqrt((1+x)/(1+x)))
- x^(sqrt((1-x)/(1-x)))
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x^3)+4*x^7-2*x
- sqrt(x)+1/x
- sqrt(x)+1/(sqrt(x))
- sqrt(x^2-8*x+17)
- sqrt(x+1)/x^3
Derivada de x^(sqrt((1-x)/(1+x)))
Solución
Ha introducido
[src]
_______
/ 1 - x
/ -----
\/ 1 + x
x
$$x^{\sqrt{\frac{1 - x}{x + 1}}}$$
x^(sqrt((1 - x)/(1 + x)))
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
/ _______ \
_______ | _______ / 1 - x / 1 1 - x \ |
/ 1 - x | / 1 - x / ----- *(1 + x)*|- --------- - ----------|*log(x)|
/ ----- | / ----- \/ 1 + x | 2*(1 + x) 2| |
\/ 1 + x |\/ 1 + x \ 2*(1 + x) / |
x *|----------- + -----------------------------------------------------|
\ x 1 - x /
$$x^{\sqrt{\frac{1 - x}{x + 1}}} \left(\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 \left(x + 1\right)}\right) \log{\left(x \right)}}{1 - x} + \frac{\sqrt{\frac{1 - x}{x + 1}}}{x}\right)$$
Segunda derivada
[src]
/ 2 \
| / / -1 + x\ \ |
____________ | / 2 \ | |-1 + ------|*log(x)| |
/ -(-1 + x) | | / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ | | 2 \ 1 + x / | |
/ ---------- | ____________ | |1 - ------| *log(x) 2*|1 - ------|*log(x) 4*|1 - ------| 2*|1 - ------|*log(x) 4*|-1 + ------|*log(x)| |- - + --------------------| *(-1 + x)|
\/ 1 + x | / -(-1 + x) | 4 \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / | \ x -1 + x / |
x *| / ---------- *|- -- + -------------------- - --------------------- + -------------- + --------------------- + ----------------------| - --------------------------------------|
|\/ 1 + x | 2 2 2 x*(-1 + x) (1 + x)*(-1 + x) (1 + x)*(-1 + x) | 1 + x |
\ \ x (-1 + x) (-1 + x) / /
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4
$$\frac{x^{\sqrt{- \frac{x - 1}{x + 1}}} \left(\sqrt{- \frac{x - 1}{x + 1}} \left(\frac{2 \left(- \frac{x - 1}{x + 1} + 1\right) \log{\left(x \right)}}{\left(x - 1\right) \left(x + 1\right)} + \frac{4 \left(\frac{x - 1}{x + 1} - 1\right) \log{\left(x \right)}}{\left(x - 1\right) \left(x + 1\right)} + \frac{\left(- \frac{x - 1}{x + 1} + 1\right)^{2} \log{\left(x \right)}}{\left(x - 1\right)^{2}} - \frac{2 \left(- \frac{x - 1}{x + 1} + 1\right) \log{\left(x \right)}}{\left(x - 1\right)^{2}} + \frac{4 \left(- \frac{x - 1}{x + 1} + 1\right)}{x \left(x - 1\right)} - \frac{4}{x^{2}}\right) - \frac{\left(x - 1\right) \left(\frac{\left(\frac{x - 1}{x + 1} - 1\right) \log{\left(x \right)}}{x - 1} - \frac{2}{x}\right)^{2}}{x + 1}\right)}{4}$$
Tercera derivada
[src]
/ / 2 \\
| / / -1 + x\ \ | / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ ||
| | |-1 + ------|*log(x)| | |1 - ------| *log(x) 2*|1 - ------|*log(x) 4*|1 - ------| 2*|1 - ------|*log(x) 4*|-1 + ------|*log(x)||
____________ | / 3 2 2 2 \ 3 | 2 \ 1 + x / | | 4 \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / ||
/ -(-1 + x) | | / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ / -1 + x\ | / / -1 + x\ \ 3*(-1 + x)*|- - + --------------------|*|- -- + -------------------- - --------------------- + -------------- + --------------------- + ----------------------||
/ ---------- | ____________ | |-1 + ------| *log(x) 8*|-1 + ------|*log(x) 6*|-1 + ------| *log(x) 6*|-1 + ------| 12*|-1 + ------| 12*|-1 + ------| 8*|-1 + ------|*log(x) 8*|-1 + ------|*log(x) 6*|-1 + ------| *log(x) 12*|-1 + ------| | 3/2 | |-1 + ------|*log(x)| \ x -1 + x / | 2 2 2 x*(-1 + x) (1 + x)*(-1 + x) (1 + x)*(-1 + x) ||
\/ 1 + x | / -(-1 + x) |16 \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / | /-(-1 + x) \ | 2 \ 1 + x / | \ x (-1 + x) (-1 + x) /|
x *| / ---------- *|-- - --------------------- - ---------------------- - ----------------------- + ---------------- + ---------------- + ---------------- - ---------------------- - ---------------------- - ----------------------- + ------------------| - |----------| *|- - + --------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------|
|\/ 1 + x | 3 3 3 3 2 2 2 2 2 2 x*(1 + x)*(-1 + x)| \ 1 + x / \ x -1 + x / 1 + x |
\ \x (-1 + x) (-1 + x) (-1 + x) x*(-1 + x) x*(-1 + x) x *(-1 + x) (1 + x)*(-1 + x) (1 + x) *(-1 + x) (1 + x)*(-1 + x) / /
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8
$$\frac{x^{\sqrt{- \frac{x - 1}{x + 1}}} \left(- \left(- \frac{x - 1}{x + 1}\right)^{\frac{3}{2}} \left(\frac{\left(\frac{x - 1}{x + 1} - 1\right) \log{\left(x \right)}}{x - 1} - \frac{2}{x}\right)^{3} + \sqrt{- \frac{x - 1}{x + 1}} \left(- \frac{8 \left(\frac{x - 1}{x + 1} - 1\right) \log{\left(x \right)}}{\left(x - 1\right) \left(x + 1\right)^{2}} - \frac{6 \left(\frac{x - 1}{x + 1} - 1\right)^{2} \log{\left(x \right)}}{\left(x - 1\right)^{2} \left(x + 1\right)} - \frac{8 \left(\frac{x - 1}{x + 1} - 1\right) \log{\left(x \right)}}{\left(x - 1\right)^{2} \left(x + 1\right)} - \frac{\left(\frac{x - 1}{x + 1} - 1\right)^{3} \log{\left(x \right)}}{\left(x - 1\right)^{3}} - \frac{6 \left(\frac{x - 1}{x + 1} - 1\right)^{2} \log{\left(x \right)}}{\left(x - 1\right)^{3}} - \frac{8 \left(\frac{x - 1}{x + 1} - 1\right) \log{\left(x \right)}}{\left(x - 1\right)^{3}} + \frac{12 \left(\frac{x - 1}{x + 1} - 1\right)}{x \left(x - 1\right) \left(x + 1\right)} + \frac{6 \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{x \left(x - 1\right)^{2}} + \frac{12 \left(\frac{x - 1}{x + 1} - 1\right)}{x \left(x - 1\right)^{2}} + \frac{12 \left(\frac{x - 1}{x + 1} - 1\right)}{x^{2} \left(x - 1\right)} + \frac{16}{x^{3}}\right) + \frac{3 \left(x - 1\right) \left(\frac{\left(\frac{x - 1}{x + 1} - 1\right) \log{\left(x \right)}}{x - 1} - \frac{2}{x}\right) \left(\frac{2 \left(- \frac{x - 1}{x + 1} + 1\right) \log{\left(x \right)}}{\left(x - 1\right) \left(x + 1\right)} + \frac{4 \left(\frac{x - 1}{x + 1} - 1\right) \log{\left(x \right)}}{\left(x - 1\right) \left(x + 1\right)} + \frac{\left(- \frac{x - 1}{x + 1} + 1\right)^{2} \log{\left(x \right)}}{\left(x - 1\right)^{2}} - \frac{2 \left(- \frac{x - 1}{x + 1} + 1\right) \log{\left(x \right)}}{\left(x - 1\right)^{2}} + \frac{4 \left(- \frac{x - 1}{x + 1} + 1\right)}{x \left(x - 1\right)} - \frac{4}{x^{2}}\right)}{x + 1}\right)}{8}$$
Gráfico