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:
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Derivada de x^2/lnx
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Derivada de √x+2
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Derivada de x^((-2)/3)
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Derivada de (logx)^2
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Expresiones idénticas
- |x^n-x^(3n)|
- módulo de x en el grado n menos x en el grado (3n)|
- |xn-x(3n)|
- |xn-x3n|
- |x^n-x^3n|
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Expresiones semejantes
- |x^n+x^(3n)|
Derivada de |x^n-x^(3n)|
Solución
Primera derivada
[src]
/ / / n\ / 3*n\\ / / n\ / 3*n\\\
|/ / 3*n\ / n\\ |im\n*x / 3*im\n*x /| / / 3*n\ / n\\ |re\n*x / 3*re\n*x /|| / 3*n n\
|\- im\x / + im\x //*|-------- - ------------| + \- re\x / + re\x //*|-------- - ------------||*sign\x - x /
\ \ x x / \ x x //
-------------------------------------------------------------------------------------------------------------------
3*n n
x - x
$$\frac{\left(\left(\frac{\operatorname{re}{\left(n x^{n}\right)}}{x} - \frac{3 \operatorname{re}{\left(n x^{3 n}\right)}}{x}\right) \left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) + \left(\frac{\operatorname{im}{\left(n x^{n}\right)}}{x} - \frac{3 \operatorname{im}{\left(n x^{3 n}\right)}}{x}\right) \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right)\right) \operatorname{sign}{\left(x^{3 n} - x^{n} \right)}}{x^{3 n} - x^{n}}$$
Segunda derivada
[src]
/ / 2 2 \ \
| |/ / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 2 n\ / 3*n\ / 2 3*n\ / n\\ / / 3*n\ / n\\ / / 2 n\ / 3*n\ / 2 3*n\ / n\\| / n / 2*n\\ / 2*n\ // / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\\ / n / 2*n\\|
-n |// / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\\ d / / n / 2*n\\\ \\- 3*im\n*x / + im\n*x // + \- 3*re\n*x / + re\n*x // - \- im\x / + im\x //*\- im\n *x / - 3*im\n*x / + 9*im\n *x / + im\n*x // - \- re\x / + re\x //*\- re\n *x / - 3*re\n*x / + 9*re\n *x / + re\n*x ///*sign\x *\-1 + x // n*\-1 + 3*x /*\\- im\x / + im\x //*\- 3*im\n*x / + im\n*x // + \- re\x / + re\x //*\- 3*re\n*x / + re\n*x ///*sign\x *\-1 + x //|
x *|\\- im\x / + im\x //*\- 3*im\n*x / + im\n*x // + \- re\x / + re\x //*\- 3*re\n*x / + re\n*x ///*--\sign\x *\-1 + x /// + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------|
| dx x / 2*n\ |
\ x*\-1 + x / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2*n\
x*\-1 + x /
$$\frac{x^{- n} \left(- \frac{n \left(3 x^{2 n} - 1\right) \left(\left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)\right) \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)}}{x \left(x^{2 n} - 1\right)} + \left(\left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)} + \frac{\left(- \left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)} - \operatorname{re}{\left(n^{2} x^{n}\right)} + 9 \operatorname{re}{\left(n^{2} x^{3 n}\right)}\right) + \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right)^{2} - \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)} - \operatorname{im}{\left(n^{2} x^{n}\right)} + 9 \operatorname{im}{\left(n^{2} x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)^{2}\right) \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)}}{x}\right)}{x \left(x^{2 n} - 1\right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| |/ / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 2 n\ / 3*n\ / 2 3*n\ / n\\ / / 3*n\ / n\\ / / 2 n\ / 3*n\ / 2 3*n\ / n\\| d / / n / 2*n\\\ / 2*n\ // / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\\ d / / n / 2*n\\\ / 2 2 \ 2 |
| 2 / / / 3*n\ / n\\ / / 3 3*n\ / 3*n\ / 2 n\ / n\ / 2 3*n\ / 3 n\\ / / 3*n\ / n\\ / / 3 3*n\ / 3*n\ / 2 n\ / n\ / 2 3*n\ / 3 n\\ / / 3*n\ / n\\ / / 2 n\ / 3*n\ / 2 3*n\ / n\\ / / 3*n\ / n\\ / / 2 n\ / 3*n\ / 2 3*n\ / n\\\ / n / 2*n\\ 2*\\- 3*im\n*x / + im\n*x // + \- 3*re\n*x / + re\n*x // - \- im\x / + im\x //*\- im\n *x / - 3*im\n*x / + 9*im\n *x / + im\n*x // - \- re\x / + re\x //*\- re\n *x / - 3*re\n*x / + 9*re\n *x / + re\n*x ///*--\sign\x *\-1 + x /// // / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\\ / 2*n 2*n\ / n / 2*n\\ 2*n*\-1 + 3*x /*\\- im\x / + im\x //*\- 3*im\n*x / + im\n*x // + \- re\x / + re\x //*\- 3*re\n*x / + re\n*x ///*--\sign\x *\-1 + x /// / 2*n\ |/ / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 2 n\ / 3*n\ / 2 3*n\ / n\\ / / 3*n\ / n\\ / / 2 n\ / 3*n\ / 2 3*n\ / n\\| / n / 2*n\\ 2 / 2*n\ // / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\\ / n / 2*n\\|
-n |// / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\ / / 3*n\ / n\\\ d / / n / 2*n\\\ \- \- im\x / + im\x //*\- 27*im\n *x / - 6*im\n*x / - 3*im\n *x / + 2*im\n*x / + 27*im\n *x / + im\n *x // - \- re\x / + re\x //*\- 27*re\n *x / - 6*re\n*x / - 3*re\n *x / + 2*re\n*x / + 27*re\n *x / + re\n *x // + 3*\- 3*im\n*x / + im\n*x //*\- im\n *x / - 3*im\n*x / + 9*im\n *x / + im\n*x // + 3*\- 3*re\n*x / + re\n*x //*\- re\n *x / - 3*re\n*x / + 9*re\n *x / + re\n*x ///*sign\x *\-1 + x // dx n*\\- im\x / + im\x //*\- 3*im\n*x / + im\n*x // + \- re\x / + re\x //*\- 3*re\n*x / + re\n*x ///*\1 - n - 3*x + 9*n*x /*sign\x *\-1 + x // dx 2*n*\-1 + 3*x /*\\- 3*im\n*x / + im\n*x // + \- 3*re\n*x / + re\n*x // - \- im\x / + im\x //*\- im\n *x / - 3*im\n*x / + 9*im\n *x / + im\n*x // - \- re\x / + re\x //*\- re\n *x / - 3*re\n*x / + 9*re\n *x / + re\n*x ///*sign\x *\-1 + x // 2*n *\-1 + 3*x / *\\- im\x / + im\x //*\- 3*im\n*x / + im\n*x // + \- re\x / + re\x //*\- 3*re\n*x / + re\n*x ///*sign\x *\-1 + x //|
x *|\\- im\x / + im\x //*\- 3*im\n*x / + im\n*x // + \- re\x / + re\x //*\- 3*re\n*x / + re\n*x ///*---\sign\x *\-1 + x /// - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------|
| 2 2 x 2 / 2*n\ / 2*n\ 2 / 2*n\ 2 |
| dx x x *\-1 + x / x*\-1 + x / x *\-1 + x / 2 / 2*n\ |
\ x *\-1 + x / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2*n\
x*\-1 + x /
$$\frac{x^{- n} \left(\frac{2 n^{2} \left(3 x^{2 n} - 1\right)^{2} \left(\left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)\right) \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)}}{x^{2} \left(x^{2 n} - 1\right)^{2}} - \frac{2 n \left(3 x^{2 n} - 1\right) \left(\left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)}}{x \left(x^{2 n} - 1\right)} - \frac{2 n \left(3 x^{2 n} - 1\right) \left(- \left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)} - \operatorname{re}{\left(n^{2} x^{n}\right)} + 9 \operatorname{re}{\left(n^{2} x^{3 n}\right)}\right) + \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right)^{2} - \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)} - \operatorname{im}{\left(n^{2} x^{n}\right)} + 9 \operatorname{im}{\left(n^{2} x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)^{2}\right) \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)}}{x^{2} \left(x^{2 n} - 1\right)} - \frac{n \left(\left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)\right) \left(9 n x^{2 n} - n - 3 x^{2 n} + 1\right) \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)}}{x^{2} \left(x^{2 n} - 1\right)} + \left(\left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)\right) \frac{\partial^{2}}{\partial x^{2}} \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)} + \frac{2 \left(- \left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)} - \operatorname{re}{\left(n^{2} x^{n}\right)} + 9 \operatorname{re}{\left(n^{2} x^{3 n}\right)}\right) + \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right)^{2} - \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)} - \operatorname{im}{\left(n^{2} x^{n}\right)} + 9 \operatorname{im}{\left(n^{2} x^{3 n}\right)}\right) + \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right)^{2}\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)}}{x} - \frac{\left(- \left(\operatorname{re}{\left(x^{n}\right)} - \operatorname{re}{\left(x^{3 n}\right)}\right) \left(2 \operatorname{re}{\left(n x^{n}\right)} - 6 \operatorname{re}{\left(n x^{3 n}\right)} - 3 \operatorname{re}{\left(n^{2} x^{n}\right)} + 27 \operatorname{re}{\left(n^{2} x^{3 n}\right)} + \operatorname{re}{\left(n^{3} x^{n}\right)} - 27 \operatorname{re}{\left(n^{3} x^{3 n}\right)}\right) + 3 \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)}\right) \left(\operatorname{re}{\left(n x^{n}\right)} - 3 \operatorname{re}{\left(n x^{3 n}\right)} - \operatorname{re}{\left(n^{2} x^{n}\right)} + 9 \operatorname{re}{\left(n^{2} x^{3 n}\right)}\right) - \left(\operatorname{im}{\left(x^{n}\right)} - \operatorname{im}{\left(x^{3 n}\right)}\right) \left(2 \operatorname{im}{\left(n x^{n}\right)} - 6 \operatorname{im}{\left(n x^{3 n}\right)} - 3 \operatorname{im}{\left(n^{2} x^{n}\right)} + 27 \operatorname{im}{\left(n^{2} x^{3 n}\right)} + \operatorname{im}{\left(n^{3} x^{n}\right)} - 27 \operatorname{im}{\left(n^{3} x^{3 n}\right)}\right) + 3 \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)}\right) \left(\operatorname{im}{\left(n x^{n}\right)} - 3 \operatorname{im}{\left(n x^{3 n}\right)} - \operatorname{im}{\left(n^{2} x^{n}\right)} + 9 \operatorname{im}{\left(n^{2} x^{3 n}\right)}\right)\right) \operatorname{sign}{\left(x^{n} \left(x^{2 n} - 1\right) \right)}}{x^{2}}\right)}{x \left(x^{2 n} - 1\right)}$$