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:
-
Derivada de 1/(x+3)
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Derivada de 4*y
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Derivada de (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- y=arctgln(sqrt(x)/(x+ dos))^ tres
- y es igual a arctgln( raíz cuadrada de (x) dividir por (x más 2)) al cubo
- y es igual a arctgln( raíz cuadrada de (x) dividir por (x más dos)) en el grado tres
- y=arctgln(√(x)/(x+2))^3
- y=arctgln(sqrt(x)/(x+2))3
- y=arctglnsqrtx/x+23
- y=arctgln(sqrt(x)/(x+2))³
- y=arctgln(sqrt(x)/(x+2)) en el grado 3
- y=arctglnsqrtx/x+2^3
- y=arctgln(sqrt(x) dividir por (x+2))^3
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Expresiones semejantes
- y=arctgln(sqrt(x)/(x-2))^3
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(a^2+x^2)/sqrt(a^2-x^2)
Derivada de y=arctgln(sqrt(x)/(x+2))^3
Solución
Ha introducido
[src]
/ / ___\\
3| |\/ x ||
atan |log|-----||
\ \x + 2//
$$\operatorname{atan}^{3}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}$$
atan(log(sqrt(x)/(x + 2)))^3
Primera derivada
[src]
/ / ___\\ / ___ \
2| |\/ x || | 1 \/ x |
3*atan |log|-----||*(x + 2)*|--------------- - --------|
\ \x + 2// | ___ 2|
\2*\/ x *(x + 2) (x + 2) /
--------------------------------------------------------
/ / ___\\
___ | 2|\/ x ||
\/ x *|1 + log |-----||
\ \x + 2//
$$\frac{3 \left(x + 2\right) \left(- \frac{\sqrt{x}}{\left(x + 2\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x + 2\right)}\right) \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{\sqrt{x} \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)}$$
Segunda derivada
[src]
/ 2 2 \
|/ ___\ / / ___\\ / ___ \ / / ___\\ / ___\ / ___\ / / ___\\ / ___\ / / ___\\ / ___\|
|| 1 2*\/ x | | |\/ x || | 1 8*\/ x 4 | | |\/ x || | 1 2*\/ x | | 1 2*\/ x | | |\/ x || | 1 2*\/ x | | |\/ x || |\/ x ||
||- ----- + -------|*atan|log|-----|| |---- - -------- + -------------|*atan|log|-----|| 2*|- ----- + -------| 2*|- ----- + -------|*atan|log|-----|| 2*|- ----- + -------| *atan|log|-----||*log|-----||
|| ___ 2 + x | \ \2 + x// | 3/2 2 ___ | \ \2 + x// | ___ 2 + x | | ___ 2 + x | \ \2 + x// | ___ 2 + x | \ \2 + x// \2 + x/| / / ___\\
|\ \/ x / \x (2 + x) \/ x *(2 + x)/ \ \/ x / \ \/ x / \ \/ x / | | |\/ x ||
3*|------------------------------------ - -------------------------------------------------- + ---------------------- - -------------------------------------- - --------------------------------------------------|*atan|log|-----||
| 3/2 ___ / / ___\\ ___ / / ___\\ | \ \2 + x//
| x \/ x | 2|\/ x || \/ x *(2 + x) | 2|\/ x || |
| x*|1 + log |-----|| x*|1 + log |-----|| |
\ \ \2 + x// \ \2 + x// /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / ___\\
| 2|\/ x ||
4*|1 + log |-----||
\ \2 + x//
$$\frac{3 \left(- \frac{2 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{2} \log{\left(\frac{\sqrt{x}}{x + 2} \right)} \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{x \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} + \frac{2 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{2}}{x \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} - \frac{\left(- \frac{8 \sqrt{x}}{\left(x + 2\right)^{2}} + \frac{4}{\sqrt{x} \left(x + 2\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{\sqrt{x}} - \frac{2 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right) \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{\sqrt{x} \left(x + 2\right)} + \frac{\left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right) \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{x^{\frac{3}{2}}}\right) \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{4 \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)}$$
Tercera derivada
[src]
/ 3 2 3 3 2 3 2 2 \
| / / ___\\ / ___\ / ___\ / / ___\\ / ___ \ / / ___\\ / ___ \ / / ___\\ / ___\ / ___\ / / ___\\ / / ___\\ / ___ \ / ___\ / / ___\\ / ___\ / / ___\\ / ___\ / ___\ / / ___\\ / ___\ / / ___\\ / ___\ / ___\ / ___ \ / / ___\\ / ___\ / / ___\\ / ___\ / ___\ / / ___\\ / ___\ / / ___\\ / ___\ / ___ \ / ___\|
| 2| |\/ x || | 1 2*\/ x | | 1 2*\/ x | 2| |\/ x || | 1 8*\/ x 4 | 2| |\/ x || | 1 16*\/ x 2 8 | 2| |\/ x || | 1 2*\/ x | | 1 2*\/ x | | |\/ x || 2| |\/ x || | 1 8*\/ x 4 | | 1 2*\/ x | 2| |\/ x || | 1 2*\/ x | 2| |\/ x || 2|\/ x | | 1 2*\/ x | | |\/ x || | 1 2*\/ x | | |\/ x || |\/ x | | 1 2*\/ x | | 1 8*\/ x 4 | | |\/ x || | 1 2*\/ x | 2| |\/ x || |\/ x | | 1 2*\/ x | 2| |\/ x || |\/ x | 2| |\/ x || | 1 2*\/ x | | 1 8*\/ x 4 | |\/ x ||
| 3*atan |log|-----||*|- ----- + -------| |- ----- + -------| atan |log|-----||*|---- - -------- + -------------| 3*atan |log|-----||*|---- - -------- + ------------ + --------------| atan |log|-----||*|- ----- + -------| 3*|- ----- + -------| *atan|log|-----|| atan |log|-----||*|---- - -------- + -------------| |- ----- + -------| *atan |log|-----|| |- ----- + -------| *atan |log|-----||*log |-----| 3*|- ----- + -------| *atan|log|-----|| 3*|- ----- + -------| *atan|log|-----||*log|-----| 3*|- ----- + -------|*|---- - -------- + -------------|*atan|log|-----|| 3*|- ----- + -------| *atan |log|-----||*log|-----| 3*|- ----- + -------| *atan |log|-----||*log|-----| 3*atan |log|-----||*|- ----- + -------|*|---- - -------- + -------------|*log|-----||
| \ \2 + x// | ___ 2 + x | | ___ 2 + x | \ \2 + x// | 3/2 2 ___ | \ \2 + x// | 5/2 3 3/2 ___ 2| \ \2 + x// | ___ 2 + x | | ___ 2 + x | \ \2 + x// \ \2 + x// | 3/2 2 ___ | | ___ 2 + x | \ \2 + x// | ___ 2 + x | \ \2 + x// \2 + x/ | ___ 2 + x | \ \2 + x// | ___ 2 + x | \ \2 + x// \2 + x/ | ___ 2 + x | | 3/2 2 ___ | \ \2 + x// | ___ 2 + x | \ \2 + x// \2 + x/ | ___ 2 + x | \ \2 + x// \2 + x/ \ \2 + x// | ___ 2 + x | | 3/2 2 ___ | \2 + x/|
| \ \/ x / \ \/ x / \x (2 + x) \/ x *(2 + x)/ \x (2 + x) x *(2 + x) \/ x *(2 + x) / \ \/ x / \ \/ x / \x (2 + x) \/ x *(2 + x)/ \ \/ x / \ \/ x / \ \/ x / \ \/ x / \ \/ x / \x (2 + x) \/ x *(2 + x)/ \ \/ x / \ \/ x / \ \/ x / \x (2 + x) \/ x *(2 + x)/ |
3*|- --------------------------------------- - ------------------------- + --------------------------------------------------- + --------------------------------------------------------------------- + ------------------------------------- - --------------------------------------- - --------------------------------------------------- + -------------------------------------- - -------------------------------------------------- + --------------------------------------- + -------------------------------------------------- + ------------------------------------------------------------------------ + --------------------------------------------------- - --------------------------------------------------- - ------------------------------------------------------------------------------------|
| 5/2 2 3/2 ___ 3/2 / / ___\\ ___ / / ___\\ 2 / / ___\\ 2 / / ___\\ / / ___\\ / / ___\\ / / ___\\ |
| 8*x / / ___\\ 4*x 8*\/ x 2*x *(2 + x) 2 | 2|\/ x || 2*\/ x *(2 + x) 3/2 | 2|\/ x || / / ___\\ | 2|\/ x || / / ___\\ | 2|\/ x || 2 | 2|\/ x || | 2|\/ x || | 2|\/ x || |
| 3/2 | 2|\/ x || 4*x *|1 + log |-----|| 4*x *|1 + log |-----|| 3/2 | 2|\/ x || 2*x*|1 + log |-----||*(2 + x) 3/2 | 2|\/ x || 4*x*|1 + log |-----|| 4*x *|1 + log |-----|| 2*x*|1 + log |-----||*(2 + x) 4*x*|1 + log |-----|| |
| 4*x *|1 + log |-----|| \ \2 + x// \ \2 + x// x *|1 + log |-----|| \ \2 + x// 2*x *|1 + log |-----|| \ \2 + x// \ \2 + x// \ \2 + x// \ \2 + x// |
\ \ \2 + x// \ \2 + x// \ \2 + x// /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ___\
2|\/ x |
1 + log |-----|
\2 + x/
$$\frac{3 \left(- \frac{3 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right) \left(- \frac{8 \sqrt{x}}{\left(x + 2\right)^{2}} + \frac{4}{\sqrt{x} \left(x + 2\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(\frac{\sqrt{x}}{x + 2} \right)} \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{4 x \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} + \frac{3 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right) \left(- \frac{8 \sqrt{x}}{\left(x + 2\right)^{2}} + \frac{4}{\sqrt{x} \left(x + 2\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{4 x \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{2} \log{\left(\frac{\sqrt{x}}{x + 2} \right)} \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{2 x \left(x + 2\right) \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} + \frac{3 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{2} \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{2 x \left(x + 2\right) \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} + \frac{3 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{2} \log{\left(\frac{\sqrt{x}}{x + 2} \right)} \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{4 x^{2} \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{2} \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{4 x^{2} \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} + \frac{3 \left(- \frac{16 \sqrt{x}}{\left(x + 2\right)^{3}} + \frac{8}{\sqrt{x} \left(x + 2\right)^{2}} + \frac{2}{x^{\frac{3}{2}} \left(x + 2\right)} + \frac{1}{x^{\frac{5}{2}}}\right) \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{8 \sqrt{x}} - \frac{\left(- \frac{8 \sqrt{x}}{\left(x + 2\right)^{2}} + \frac{4}{\sqrt{x} \left(x + 2\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{2 \sqrt{x} \left(x + 2\right)} + \frac{\left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{3} \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{4 x^{\frac{3}{2}} \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)} - \frac{\left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{3} \log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{x^{\frac{3}{2}} \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)^{2}} + \frac{3 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{3} \log{\left(\frac{\sqrt{x}}{x + 2} \right)} \operatorname{atan}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{2 x^{\frac{3}{2}} \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)^{2}} - \frac{\left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right)^{3}}{4 x^{\frac{3}{2}} \left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1\right)^{2}} + \frac{\left(- \frac{8 \sqrt{x}}{\left(x + 2\right)^{2}} + \frac{4}{\sqrt{x} \left(x + 2\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{4 x^{\frac{3}{2}}} + \frac{\left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right) \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{2 x^{\frac{3}{2}} \left(x + 2\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x + 2} - \frac{1}{\sqrt{x}}\right) \operatorname{atan}^{2}{\left(\log{\left(\frac{\sqrt{x}}{x + 2} \right)} \right)}}{8 x^{\frac{5}{2}}}\right)}{\log{\left(\frac{\sqrt{x}}{x + 2} \right)}^{2} + 1}$$
Gráfico