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^-0,2
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Derivada de e-x
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Derivada de e^e
- Derivada de e^((3*x)^2)
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Expresiones idénticas
- y=arctg*ln*(sqrtx/x+ dos)^ tres
- y es igual a arctg multiplicar por ln multiplicar por ( raíz cuadrada de x dividir por x más 2) al cubo
- y es igual a arctg multiplicar por ln multiplicar por ( raíz cuadrada de x dividir por x más dos) en el grado tres
- y=arctg*ln*(√x/x+2)^3
- y=arctg*ln*(sqrtx/x+2)3
- y=arctg*ln*sqrtx/x+23
- y=arctg*ln*(sqrtx/x+2)³
- y=arctg*ln*(sqrtx/x+2) en el grado 3
- y=arctgln(sqrtx/x+2)^3
- y=arctgln(sqrtx/x+2)3
- y=arctglnsqrtx/x+23
- y=arctglnsqrtx/x+2^3
- y=arctg*ln*(sqrtx dividir por x+2)^3
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Expresiones semejantes
- y=arctg*ln*(sqrtx/x-2)^3
Derivada de y=arctg*ln*(sqrtx/x+2)^3
Solución
Ha introducido
[src]
/ ___ \
3|\/ x |
atan(x)*log |----- + 2|
\ x /
$$\log{\left(\frac{\sqrt{x}}{x} + 2 \right)}^{3} \operatorname{atan}{\left(x \right)}$$
atan(x)*log(sqrt(x)/x + 2)^3
Primera derivada
[src]
/ ___ \ / ___ \
3|\/ x | 2|\/ x |
log |----- + 2| 3*log |----- + 2|*atan(x)
\ x / \ x /
--------------- - -------------------------
2 / ___ \
1 + x 3/2 |\/ x |
2*x *|----- + 2|
\ x /
$$\frac{\log{\left(\frac{\sqrt{x}}{x} + 2 \right)}^{3}}{x^{2} + 1} - \frac{3 \log{\left(\frac{\sqrt{x}}{x} + 2 \right)}^{2} \operatorname{atan}{\left(x \right)}}{2 x^{\frac{3}{2}} \left(\frac{\sqrt{x}}{x} + 2\right)}$$
Segunda derivada
[src]
/ / / 1 \ / 1 \\ \ | | 3*log|2 + -----| log|2 + -----|| | | | | ___| | ___|| | | | 2 \ \/ x / \ \/ x /| | | 3*|-------------- + ---------------- - --------------|*atan(x) | | 2/ 1 \ | 3 / 1 \ 5/2 3 / 1 \| / 1 \ | | 2*x*log |2 + -----| |x *|2 + -----| x x *|2 + -----|| 3*log|2 + -----| | | | ___| | | ___| | ___|| | ___| | | \ \/ x / \ \ \/ x / \ \/ x // \ \/ x / | / 1 \ |- ------------------- + -------------------------------------------------------------- - -------------------------|*log|2 + -----| | 2 / 1 \ 3/2 / 2\ / 1 \| | ___| | / 2\ 4*|2 + -----| x *\1 + x /*|2 + -----|| \ \/ x / | \1 + x / | ___| | ___|| \ \ \/ x / \ \/ x //
$$\left(- \frac{2 x \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(- \frac{\log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{3} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{2}{x^{3} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{3 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{\frac{5}{2}}}\right) \operatorname{atan}{\left(x \right)}}{4 \left(2 + \frac{1}{\sqrt{x}}\right)} - \frac{3 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{\frac{3}{2}} \left(2 + \frac{1}{\sqrt{x}}\right) \left(x^{2} + 1\right)}\right) \log{\left(2 + \frac{1}{\sqrt{x}} \right)}$$
Tercera derivada
[src]
/ 2/ 1 \ 2/ 1 \ / 1 \ 2/ 1 \ / 1 \\
| 15*log |2 + -----| 9*log |2 + -----| 6*log|2 + -----| 2*log |2 + -----| 18*log|2 + -----|| / / 1 \ / 1 \\
| | ___| | ___| | ___| | ___| | ___|| | 3*log|2 + -----| log|2 + -----||
| 2 \ \/ x / \ \/ x / \ \/ x / \ \/ x / \ \/ x /| | | ___| | ___||
3*|----------------- + ------------------ - ----------------- - ----------------- + ----------------- + -----------------|*atan(x) | 2 \ \/ x / \ \/ x /| / 1 \
/ 2 \ | 2 7/2 4 / 1 \ 2 2 4 / 1 \ | 9*|-------------- + ---------------- - --------------|*log|2 + -----|
3/ 1 \ | 4*x | | 9/2 / 1 \ x x *|2 + -----| 9/2 / 1 \ 9/2 / 1 \ x *|2 + -----| | 2/ 1 \ | 3 / 1 \ 5/2 3 / 1 \| | ___|
2*log |2 + -----|*|-1 + ------| |x *|2 + -----| | ___| x *|2 + -----| x *|2 + -----| | ___| | 9*log |2 + -----| |x *|2 + -----| x x *|2 + -----|| \ \/ x /
| ___| | 2| | | ___| \ \/ x / | ___| | ___| \ \/ x / | | ___| | | ___| | ___||
\ \/ x / \ 1 + x / \ \ \/ x / \ \/ x / \ \/ x / / \ \/ x / \ \ \/ x / \ \/ x //
------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------- + --------------------------- + ---------------------------------------------------------------------
2 / 1 \ 2 / 2\ / 1 \
/ 2\ 8*|2 + -----| ___ / 2\ / 1 \ 4*\1 + x /*|2 + -----|
\1 + x / | ___| \/ x *\1 + x / *|2 + -----| | ___|
\ \/ x / | ___| \ \/ x /
\ \/ x /
$$\frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{3}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(- \frac{9 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{x^{4} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{18 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{4} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{15 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{x^{\frac{7}{2}}} + \frac{2 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{x^{\frac{9}{2}} \left(2 + \frac{1}{\sqrt{x}}\right)^{2}} - \frac{6 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{\frac{9}{2}} \left(2 + \frac{1}{\sqrt{x}}\right)^{2}} + \frac{2}{x^{\frac{9}{2}} \left(2 + \frac{1}{\sqrt{x}}\right)^{2}}\right) \operatorname{atan}{\left(x \right)}}{8 \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{9 \left(- \frac{\log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{3} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{2}{x^{3} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{3 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{\frac{5}{2}}}\right) \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{4 \left(2 + \frac{1}{\sqrt{x}}\right) \left(x^{2} + 1\right)} + \frac{9 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{\sqrt{x} \left(2 + \frac{1}{\sqrt{x}}\right) \left(x^{2} + 1\right)^{2}}$$
Gráfico