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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 y=(x^2-3^3)
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Derivada de y=(x^2−2)(x^7+4)
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Derivada de y=x^2+2^x
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Derivada de y=(x²+2x+4)*(x-2)
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Expresiones idénticas
- x*sqr(uno -x^ dos)+arctg(x/sqr(uno -x^ dos))
- x multiplicar por sqr(1 menos x al cuadrado ) más arctg(x dividir por sqr(1 menos x al cuadrado ))
- x multiplicar por sqr(uno menos x en el grado dos) más arctg(x dividir por sqr(uno menos x en el grado dos))
- x*sqr(1-x2)+arctg(x/sqr(1-x2))
- x*sqr1-x2+arctgx/sqr1-x2
- x*sqr(1-x²)+arctg(x/sqr(1-x²))
- x*sqr(1-x en el grado 2)+arctg(x/sqr(1-x en el grado 2))
- xsqr(1-x^2)+arctg(x/sqr(1-x^2))
- xsqr(1-x2)+arctg(x/sqr(1-x2))
- xsqr1-x2+arctgx/sqr1-x2
- xsqr1-x^2+arctgx/sqr1-x^2
- x*sqr(1-x^2)+arctg(x dividir por sqr(1-x^2))
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Expresiones semejantes
- x*sqr(1-x^2)+arctg(x/sqr(1+x^2))
- x*sqr(1-x^2)-arctg(x/sqr(1-x^2))
- x*sqr(1+x^2)+arctg(x/sqr(1-x^2))
Derivada de x*sqr(1-x^2)+arctg(x/sqr(1-x^2))
Solución
Ha introducido
[src]
/ 2\ 2/ x \
x*\1 - x / + atan |---------|
| 2|
|/ 2\ |
\\1 - x / /
$$x \left(1 - x^{2}\right) + \operatorname{atan}^{2}{\left(\frac{x}{\left(1 - x^{2}\right)^{2}} \right)}$$
x*(1 - x^2) + atan(x/(1 - x^2)^2)^2
Primera derivada
[src]
/ 2 \
| 1 4*x | / x \
2*|--------- + ---------|*atan|---------|
| 2 3| | 2|
|/ 2\ / 2\ | |/ 2\ |
2 \\1 - x / \1 - x / / \\1 - x / /
1 - 3*x + -----------------------------------------
2
x
1 + ---------
4
/ 2\
\1 - x /
$$- 3 x^{2} + 1 + \frac{2 \left(\frac{4 x^{2}}{\left(1 - x^{2}\right)^{3}} + \frac{1}{\left(1 - x^{2}\right)^{2}}\right) \operatorname{atan}{\left(\frac{x}{\left(1 - x^{2}\right)^{2}} \right)}}{\frac{x^{2}}{\left(1 - x^{2}\right)^{4}} + 1}$$
Segunda derivada
[src]
/ 2 \ | 2 / 2 \ / 2 \ | | / 2 \ | 4*x | / x \ | 2*x | / x \| | | 4*x | 2*x*|-1 + -------| *atan|----------| 12*x*|-1 + -------|*atan|----------|| | |-1 + -------| | 2| | 2| | 2| | 2|| | | 2| \ -1 + x / |/ 2\ | \ -1 + x / |/ 2\ || | \ -1 + x / \\-1 + x / / \\-1 + x / /| 2*|-3*x + ---------------------------- - ------------------------------------ + ------------------------------------| | 2 2 / 2 \ 3 | | / 2 \ 4 / 2 \ 6 | x | / 2\ | | | x | / 2\ | x | / 2\ |1 + ----------|*\-1 + x / | | |1 + ----------| *\-1 + x / |1 + ----------| *\-1 + x / | 4| | | | 4| | 4| | / 2\ | | | | / 2\ | | / 2\ | \ \-1 + x / / | \ \ \-1 + x / / \ \-1 + x / / /
$$2 \left(- 3 x + \frac{12 x \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{3} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)} - \frac{2 x \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{2} \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{6} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{2}}{\left(x^{2} - 1\right)^{4} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}}\right)$$
Tercera derivada
[src]
/ 3 \ | / 2 4 \ 3 / 2 \ / 2 \ / 2 4 \ / 2 \ / 2 \ | | | 12*x 16*x | / x \ / 2 \ / 2 \ / 2 \ 2 | 4*x | / x \ | 4*x | | 20*x 40*x | / x \ 2 | 2*x | | 4*x | / x \| | 12*|1 - ------- + ----------|*atan|----------| | 4*x | | 2*x | | 4*x | 8*x *|-1 + -------| *atan|----------| 2*|-1 + -------|*|1 - ------- + ----------|*atan|----------| 48*x *|-1 + -------|*|-1 + -------|*atan|----------|| | | 2 2| | 2| 6*x*|-1 + -------| 36*x*|-1 + -------|*|-1 + -------| | 2| | 2| | 2| | 2 2| | 2| | 2| | 2| | 2|| | | -1 + x / 2\ | |/ 2\ | | 2| | 2| | 2| \ -1 + x / |/ 2\ | \ -1 + x / | -1 + x / 2\ | |/ 2\ | \ -1 + x / \ -1 + x / |/ 2\ || | \ \-1 + x / / \\-1 + x / / \ -1 + x / \ -1 + x / \ -1 + x / \\-1 + x / / \ \-1 + x / / \\-1 + x / / \\-1 + x / /| 2*|-3 - ---------------------------------------------- + ---------------------------- - ---------------------------------- - ------------------------------------- + ------------------------------------------------------------ + ----------------------------------------------------| | / 2 \ 3 3 2 3 2 2 | | | x | / 2\ / 2 \ 8 / 2 \ 5 / 2 \ 10 / 2 \ 6 / 2 \ 7 | | |1 + ----------|*\-1 + x / | x | / 2\ | x | / 2\ | x | / 2\ | x | / 2\ | x | / 2\ | | | 4| |1 + ----------| *\-1 + x / |1 + ----------| *\-1 + x / |1 + ----------| *\-1 + x / |1 + ----------| *\-1 + x / |1 + ----------| *\-1 + x / | | | / 2\ | | 4| | 4| | 4| | 4| | 4| | | \ \-1 + x / / | / 2\ | | / 2\ | | / 2\ | | / 2\ | | / 2\ | | \ \ \-1 + x / / \ \-1 + x / / \ \-1 + x / / \ \-1 + x / / \ \-1 + x / / /
$$2 \left(\frac{48 x^{2} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right) \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{7} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}} - \frac{8 x^{2} \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{3} \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{10} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{3}} - \frac{36 x \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right) \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{5} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}} + \frac{6 x \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{3}}{\left(x^{2} - 1\right)^{8} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{3}} - 3 - \frac{12 \left(\frac{16 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{12 x^{2}}{x^{2} - 1} + 1\right) \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{3} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)} + \frac{2 \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right) \left(\frac{40 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{20 x^{2}}{x^{2} - 1} + 1\right) \operatorname{atan}{\left(\frac{x}{\left(x^{2} - 1\right)^{2}} \right)}}{\left(x^{2} - 1\right)^{6} \left(\frac{x^{2}}{\left(x^{2} - 1\right)^{4}} + 1\right)^{2}}\right)$$
Gráfico