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^4/3-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
- x×sqrt(uno -x²)/(uno +x²)- tres /sqrt(dos)×arctg(xsqrt(dos)/sqrt(uno -x²))
- x× raíz cuadrada de (1 menos x²) dividir por (1 más x²) menos 3 dividir por raíz cuadrada de (2)×arctg(x raíz cuadrada de (2) dividir por raíz cuadrada de (1 menos x²))
- x× raíz cuadrada de (uno menos x²) dividir por (uno más x²) menos tres dividir por raíz cuadrada de (dos)×arctg(x raíz cuadrada de (dos) dividir por raíz cuadrada de (uno menos x²))
- x×√(1-x²)/(1+x²)-3/√(2)×arctg(x√(2)/√(1-x²))
- x×sqrt1-x²/1+x²-3/sqrt2×arctgxsqrt2/sqrt1-x²
- x×sqrt(1-x²) dividir por (1+x²)-3 dividir por sqrt(2)×arctg(xsqrt(2) dividir por sqrt(1-x²))
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Expresiones semejantes
- x×sqrt(1-x²)/(1+x²)+3/sqrt(2)×arctg(xsqrt(2)/sqrt(1-x²))
- x×sqrt(1+x²)/(1+x²)-3/sqrt(2)×arctg(xsqrt(2)/sqrt(1-x²))
- x×sqrt(1-x²)/(1+x²)-3/sqrt(2)×arctg(xsqrt(2)/sqrt(1+x²))
- x×sqrt(1-x²)/(1-x²)-3/sqrt(2)×arctg(xsqrt(2)/sqrt(1-x²))
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Expresiones con funciones
- xsqrt
- xsqrt(x)-3x+1
- xsqrt(x^2+x+1)
- xsqrt((x^2-x+1))
- xsqrt(x^2+3)
- xsqrt(x^2+4)
Derivada de x×sqrt(1-x²)/(1+x²)-3/sqrt(2)×arctg(xsqrt(2)/sqrt(1-x²))
Solución
Ha introducido
[src]
________
/ 2 / ___ \
x*\/ 1 - x 3 | x*\/ 2 |
------------- - -----*atan|-----------|
2 ___ | ________|
1 + x \/ 2 | / 2 |
\\/ 1 - x /
$$\frac{x \sqrt{1 - x^{2}}}{x^{2} + 1} - \frac{3}{\sqrt{2}} \operatorname{atan}{\left(\frac{\sqrt{2} x}{\sqrt{1 - x^{2}}} \right)}$$
(x*sqrt(1 - x^2))/(1 + x^2) - 3/sqrt(2)*atan((x*sqrt(2))/sqrt(1 - x^2))
Primera derivada
[src]
________ 2 / ___ ___ 2 \
/ 2 x ___ | \/ 2 \/ 2 *x |
\/ 1 - x - ----------- 3*\/ 2 *|----------- + -----------|
________ ________ | ________ 3/2|
/ 2 2 / 2 | / 2 / 2\ |
\/ 1 - x 2*x *\/ 1 - x \\/ 1 - x \1 - x / /
------------------------- - ---------------- - -----------------------------------
2 2 / 2 \
1 + x / 2\ | 2*x |
\1 + x / 2*|1 + ------|
| 2|
\ 1 - x /
$$- \frac{2 x^{2} \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \sqrt{2} \left(\frac{\sqrt{2} x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\sqrt{2}}{\sqrt{1 - x^{2}}}\right)}{2 \left(\frac{2 x^{2}}{1 - x^{2}} + 1\right)} + \frac{- \frac{x^{2}}{\sqrt{1 - x^{2}}} + \sqrt{1 - x^{2}}}{x^{2} + 1}$$
Segunda derivada
[src]
/ / ________ 2 \ \ | | / 2 x | 2 / 2 \ / 2 \ / 2 \ | | 2*|- \/ 1 - x + -----------| x | x | | x | | x | | | ________ | ________| 3 + ------ ________ 9*|1 + ------| 12*|1 + ------|*|-1 + -------| | | / 2 | / 2 | 2 2 2 / 2 | 2| | 2| | 2| | | 4*\/ 1 - x \ \/ 1 - x / 1 - x 2*x 8*x *\/ 1 - x \ 1 - x / \ 1 - x / \ -1 + x / | x*|- ------------- + ------------------------------- - -------------------- + --------------------- + ---------------- + -------------------------- + -------------------------------------| | 2 2 ________ 2 ________ 3 3/2 / 2 \ 2| | / 2\ / 2\ / 2\ / 2 / 2\ / 2 / 2\ / 2\ | 2*x | ________ / 2 \ | | \1 + x / \1 + x / \1 + x /*\/ 1 - x \1 + x / *\/ 1 - x \1 + x / \1 - x / *|-1 + -------| / 2 / 2\ | 2*x | | | | 2| \/ 1 - x *\-1 + x /*|-1 + -------| | | \ -1 + x / | 2| | \ \ -1 + x / /
$$x \left(\frac{8 x^{2} \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{3}} + \frac{2 x^{2}}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{2}} - \frac{4 \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{\frac{x^{2}}{1 - x^{2}} + 3}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)} + \frac{12 \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right) \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)^{2}} + \frac{9 \left(\frac{x^{2}}{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}\right)$$
Tercera derivada
[src]
/ ________ 2 \ / ________ 2 \ / 4 2 \ / 4 2 \ / 2 \ / 2 4 \ 2
| / 2 x | 2 | / 2 x | | x 2*x | | 5*x 6*x | / 2 \ | x | | 5*x 4*x | / 2 \ / 2 \ / 2 \ / 2 \
2*|- \/ 1 - x + -----------| 8*x *|- \/ 1 - x + -----------| 3*|1 + --------- + ------| 9*|1 + --------- + ------| 2 | x | 12*|1 + ------|*|1 - ------- + ----------| 2 | x | | x | 2 | x | | x |
________ | ________| ________ | ________| | 2 2| | 2 2| ________ 4*x *|3 + ------| | 2| | 2 2| 72*x *|1 + ------|*|-1 + -------| 96*x *|-1 + -------| *|1 + ------|
/ 2 | / 2 | 4 / 2 4 | / 2 | | / 2\ 1 - x | 4 | / 2\ 1 - x | 2 2 / 2 | 2| \ 1 - x / | -1 + x / 2\ | | 2| | 2| | 2| | 2|
4*\/ 1 - x \ \/ 1 - x / 48*x *\/ 1 - x 16*x \ \/ 1 - x / \ \1 - x / / 2*x \ \1 - x / / 10*x 40*x *\/ 1 - x \ 1 - x / \ \-1 + x / / \ 1 - x / \ -1 + x / \ -1 + x / \ 1 - x /
- ------------- + ------------------------------- - ----------------- - --------------------- - ---------------------------------- - -------------------------- + --------------------- + -------------------------- + --------------------- + ----------------- + --------------------- - ------------------------------------------ + ------------------------------------- + --------------------------------------
2 2 4 3 ________ 3 ________ 2 3/2 3/2 / 2 \ 2 ________ 3 2 ________ 2 2 3
/ 2\ / 2\ / 2\ / 2\ / 2 / 2\ / 2\ / 2 / 2\ / 2\ / 2\ | 2*x | / 2\ / 2 / 2\ / 2\ / 2 ________ / 2 \ 3/2 / 2 \ ________ 2 / 2 \
\1 + x / \1 + x / \1 + x / \1 + x / *\/ 1 - x \1 + x / \1 + x /*\/ 1 - x \1 + x / *\1 - x / \1 - x / *|-1 + -------| \1 + x / *\/ 1 - x \1 + x / \1 + x / *\/ 1 - x / 2 / 2\ | 2*x | / 2\ / 2\ | 2*x | / 2 / 2\ | 2*x |
| 2| \/ 1 - x *\-1 + x /*|-1 + -------| \1 - x / *\-1 + x /*|-1 + -------| \/ 1 - x *\-1 + x / *|-1 + -------|
\ -1 + x / | 2| | 2| | 2|
\ -1 + x / \ -1 + x / \ -1 + x /
$$- \frac{48 x^{4} \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{4}} - \frac{16 x^{4}}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{3}} + \frac{2 x^{4}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{2} + 1\right)^{2}} + \frac{40 x^{2} \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{3}} - \frac{8 x^{2} \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)}{\left(x^{2} + 1\right)^{3}} + \frac{4 x^{2} \left(\frac{x^{2}}{1 - x^{2}} + 3\right)}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{2}} + \frac{10 x^{2}}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{2}} + \frac{96 x^{2} \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)^{2}}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right)^{2} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)^{3}} + \frac{72 x^{2} \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{2} - 1\right) \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)^{2}} - \frac{4 \sqrt{1 - x^{2}}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(\frac{x^{2}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(\frac{x^{4}}{\left(1 - x^{2}\right)^{2}} + \frac{2 x^{2}}{1 - x^{2}} + 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)} - \frac{12 \left(\frac{x^{2}}{1 - x^{2}} + 1\right) \left(\frac{4 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{5 x^{2}}{x^{2} - 1} + 1\right)}{\sqrt{1 - x^{2}} \left(x^{2} - 1\right) \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)^{2}} + \frac{9 \left(\frac{5 x^{4}}{\left(1 - x^{2}\right)^{2}} + \frac{6 x^{2}}{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}$$
Gráfico