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
-
¿Cómo usar?
- Derivada de:
-
Derivada de e^x*sin(x)
- Derivada de x!
-
Derivada de e^x*x^3
-
Derivada de e^x/x^2
-
Expresiones idénticas
- y=arctg^ tres (lnx^ uno / dos /(x+ dos))
- y es igual a arctg al cubo (lnx en el grado 1 dividir por 2 dividir por (x más 2))
- y es igual a arctg en el grado tres (lnx en el grado uno dividir por dos dividir por (x más dos))
- y=arctg3(lnx1/2/(x+2))
- y=arctg3lnx1/2/x+2
- y=arctg³(lnx^1/2/(x+2))
- y=arctg en el grado 3(lnx en el grado 1/2/(x+2))
- y=arctg^3lnx^1/2/x+2
- y=arctg^3(lnx^1 dividir por 2 dividir por (x+2))
-
Expresiones semejantes
- y=arctg^3(lnx^1/2/(x-2))
-
Expresiones con funciones
- arctg
- arctg(sqrt(x))
- arctg(cos(x))
- arctg(x+cosx)
- arctg^2(1/x)
Derivada de y=arctg^3(lnx^1/2/(x+2))
Solución
Ha introducido
[src]
/ ________\
3|\/ log(x) |
atan |----------|
\ x + 2 /
$$\operatorname{atan}^{3}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}$$
atan(sqrt(log(x))/(x + 2))^3
Primera derivada
[src]
/ ________\ / ________ \
2|\/ log(x) | | \/ log(x) 1 |
3*atan |----------|*|- ---------- + ----------------------|
\ x + 2 / | 2 ________|
\ (x + 2) 2*x*(x + 2)*\/ log(x) /
-----------------------------------------------------------
log(x)
1 + --------
2
(x + 2)
$$\frac{3 \left(- \frac{\sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{2}} + \frac{1}{2 x \left(x + 2\right) \sqrt{\log{\left(x \right)}}}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}}$$
Segunda derivada
[src]
/ 2 \
| / ________\ / ________\ / ________\|
| | 1 2*\/ log(x) | / 1 2*log(x)\ | 1 2*\/ log(x) | |\/ log(x) ||
| 2*|- ------------ + ------------| 2*|- - + --------|*|- ------------ + ------------|*atan|----------||
| / ________ \ / ________\ | ________ 2 + x | \ x 2 + x / | ________ 2 + x | \ 2 + x /| / ________\
| | 1 8*\/ log(x) 2 4 | |\/ log(x) | \ x*\/ log(x) / \ x*\/ log(x) / | |\/ log(x) |
3*|- |------------ - ------------ + ------------- + --------------------|*atan|----------| + ---------------------------------- - -------------------------------------------------------------------|*atan|----------|
| | 2 3/2 2 2 ________ ________| \ 2 + x / / log(x) \ / log(x) \ 2 | \ 2 + x /
| \x *log (x) (2 + x) x *\/ log(x) x*(2 + x)*\/ log(x) / |1 + --------|*(2 + x) |1 + --------|*(2 + x) |
| | 2| | 2| |
\ \ (2 + x) / \ (2 + x) / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ log(x) \
4*|1 + --------|*(2 + x)
| 2|
\ (2 + x) /
$$\frac{3 \left(- \left(- \frac{8 \sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{2}} + \frac{4}{x \left(x + 2\right) \sqrt{\log{\left(x \right)}}} + \frac{2}{x^{2} \sqrt{\log{\left(x \right)}}} + \frac{1}{x^{2} \log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)} + \frac{2 \left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right)^{2}}{\left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)} - \frac{2 \left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right) \left(\frac{2 \log{\left(x \right)}}{x + 2} - \frac{1}{x}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{\left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{4 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)}$$
Tercera derivada
[src]
/ 3 2 \
| / ________\ / ________ \ / ________\ 2 / ________\ / ________\ / ________\ / ________ \ / ________\ / ________\ / ________\ / ________\ / ________\ / ________ \ / ________\|
| 2|\/ log(x) | | 48*\/ log(x) 3 6 8 6 12 24 | | 1 2*\/ log(x) | / 1 2*log(x)\ 2|\/ log(x) | | 1 2*\/ log(x) | 2|\/ log(x) | / 1 2*log(x)\ | 1 8*\/ log(x) 2 4 | 2|\/ log(x) | | 1 2*\/ log(x) | /1 6*log(x) 4 \ | 1 2*\/ log(x) | / 1 2*log(x)\ |\/ log(x) | | 1 2*\/ log(x) | | 1 8*\/ log(x) 2 4 | |\/ log(x) ||
|atan |----------|*|- ------------- + ------------ + ------------ + ------------- + -------------------- + --------------------- + ---------------------| |- ------------ + ------------| |- - + --------| *atan |----------|*|- ------------ + ------------| atan |----------|*|- - + --------|*|------------ - ------------ + ------------- + --------------------| atan |----------|*|- ------------ + ------------|*|-- - -------- + ---------| 3*|- ------------ + ------------| *|- - + --------|*atan|----------| 3*|- ------------ + ------------|*|------------ - ------------ + ------------- + --------------------|*atan|----------||
| \ 2 + x / | 3 3 5/2 3 3/2 3 ________ 2 3/2 2 ________ 2 ________| | ________ 2 + x | \ x 2 + x / \ 2 + x / | ________ 2 + x | \ 2 + x / \ x 2 + x / | 2 3/2 2 2 ________ ________| \ 2 + x / | ________ 2 + x | | 2 2 x*(2 + x)| | ________ 2 + x | \ x 2 + x / \ 2 + x / | ________ 2 + x | | 2 3/2 2 2 ________ ________| \ 2 + x /|
| \ (2 + x) x *log (x) x *log (x) x *\/ log(x) x *(2 + x)*log (x) x *(2 + x)*\/ log(x) x*(2 + x) *\/ log(x) / \ x*\/ log(x) / \ x*\/ log(x) / \x *log (x) (2 + x) x *\/ log(x) x*(2 + x)*\/ log(x) / \ x*\/ log(x) / \x (2 + x) / \ x*\/ log(x) / \ x*\/ log(x) / \x *log (x) (2 + x) x *\/ log(x) x*(2 + x)*\/ log(x) / |
3*|-------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------- - ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------- + -------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------|
| 8 2 2 / log(x) \ 2 / log(x) \ 2 2 / log(x) \ |
| / log(x) \ 2 / log(x) \ 4 2*|1 + --------|*(2 + x) 2*|1 + --------|*(2 + x) / log(x) \ 3 4*|1 + --------|*(2 + x) |
| 4*|1 + --------| *(2 + x) |1 + --------| *(2 + x) | 2| | 2| 2*|1 + --------| *(2 + x) | 2| |
| | 2| | 2| \ (2 + x) / \ (2 + x) / | 2| \ (2 + x) / |
\ \ (2 + x) / \ (2 + x) / \ (2 + x) / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ log(x) \
|1 + --------|*(2 + x)
| 2|
\ (2 + x) /
$$\frac{3 \left(\frac{\left(- \frac{48 \sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{3}} + \frac{24}{x \left(x + 2\right)^{2} \sqrt{\log{\left(x \right)}}} + \frac{12}{x^{2} \left(x + 2\right) \sqrt{\log{\left(x \right)}}} + \frac{6}{x^{2} \left(x + 2\right) \log{\left(x \right)}^{\frac{3}{2}}} + \frac{8}{x^{3} \sqrt{\log{\left(x \right)}}} + \frac{6}{x^{3} \log{\left(x \right)}^{\frac{3}{2}}} + \frac{3}{x^{3} \log{\left(x \right)}^{\frac{5}{2}}}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{8} + \frac{3 \left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right) \left(- \frac{8 \sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{2}} + \frac{4}{x \left(x + 2\right) \sqrt{\log{\left(x \right)}}} + \frac{2}{x^{2} \sqrt{\log{\left(x \right)}}} + \frac{1}{x^{2} \log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{4 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)} - \frac{\left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right) \left(- \frac{6 \log{\left(x \right)}}{\left(x + 2\right)^{2}} + \frac{4}{x \left(x + 2\right)} + \frac{1}{x^{2}}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}} - \frac{\left(\frac{2 \log{\left(x \right)}}{x + 2} - \frac{1}{x}\right) \left(- \frac{8 \sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{2}} + \frac{4}{x \left(x + 2\right) \sqrt{\log{\left(x \right)}}} + \frac{2}{x^{2} \sqrt{\log{\left(x \right)}}} + \frac{1}{x^{2} \log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}} - \frac{\left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right)^{3}}{4 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{2}} + \frac{3 \left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right)^{2} \left(\frac{2 \log{\left(x \right)}}{x + 2} - \frac{1}{x}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{3}} - \frac{\left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right) \left(\frac{2 \log{\left(x \right)}}{x + 2} - \frac{1}{x}\right)^{2} \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{\left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{4}}\right)}{\left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)}$$
Gráfico