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 d/dx(x)
- Derivada de c/x
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Derivada de (cos(x))^x^2
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Derivada de (8*x-15)^5
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Expresiones idénticas
- y=sqrt(arctg*sqrt(x))
- y es igual a raíz cuadrada de (arctg multiplicar por raíz cuadrada de (x))
- y=√(arctg*√(x))
- y=sqrt(arctgsqrt(x))
- y=sqrtarctgsqrtx
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Expresiones semejantes
- y=sqrtarctgsqrtx
Derivada de y=sqrt(arctg*sqrt(x))
Solución
Ha introducido
[src]
_______________ / ___ \/ atan(x)*\/ x
$$\sqrt{\sqrt{x} \operatorname{atan}{\left(x \right)}}$$
sqrt(atan(x)*sqrt(x))
Primera derivada
[src]
_______________ / ___ \
/ ___ | \/ x atan(x)|
\/ \/ x *atan(x) *|---------- + -------|
| / 2\ ___|
\2*\1 + x / 4*\/ x /
-----------------------------------------
___
\/ x *atan(x)
$$\frac{\sqrt{\sqrt{x} \operatorname{atan}{\left(x \right)}} \left(\frac{\sqrt{x}}{2 \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{4 \sqrt{x}}\right)}{\sqrt{x} \operatorname{atan}{\left(x \right)}}$$
Segunda derivada
[src]
/ / 3/2 \ 2 \
| / ___\ |atan(x) 4 8*x | / ___\ / ___\ |
| |atan(x) 2*\/ x | 2*|------- - -------------- + ---------| |atan(x) 2*\/ x | |atan(x) 2*\/ x | |
| 2*|------- + -------| | 3/2 ___ / 2\ 2| |------- + -------| 4*|------- + -------| |
_______________ | | ___ 2| | x \/ x *\1 + x / / 2\ | | ___ 2| | ___ 2| |
/ ___ | \ \/ x 1 + x / \ \1 + x / / \ \/ x 1 + x / \ \/ x 1 + x / |
\/ \/ x *atan(x) *|- --------------------- - ---------------------------------------- + -------------------- - ----------------------|
| 3/2 ___ x*atan(x) ___ / 2\ |
\ x \/ x \/ x *\1 + x /*atan(x)/
---------------------------------------------------------------------------------------------------------------------------------------
16*atan(x)
$$\frac{\sqrt{\sqrt{x} \operatorname{atan}{\left(x \right)}} \left(\frac{\left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)^{2}}{x \operatorname{atan}{\left(x \right)}} - \frac{2 \left(\frac{8 x^{\frac{3}{2}}}{\left(x^{2} + 1\right)^{2}} - \frac{4}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{x^{\frac{3}{2}}}\right)}{\sqrt{x}} - \frac{4 \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)}{\sqrt{x} \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - \frac{2 \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)}{x^{\frac{3}{2}}}\right)}{16 \operatorname{atan}{\left(x \right)}}$$
Tercera derivada
[src]
/ / ___ 5/2 \ / 3/2 \ 3 2 2 / ___\ / 3/2 \ / 3/2 \ \
| | 40*\/ x 6 3*atan(x) 64*x | |atan(x) 4 8*x | / ___\ / ___\ / ___\ / ___\ |atan(x) 2*\/ x | |atan(x) 4 8*x | / ___\ |atan(x) 4 8*x | / ___\ / ___\ |
|4*|- --------- - ------------- + --------- + ---------| 8*|------- - -------------- + ---------| |atan(x) 2*\/ x | |atan(x) 2*\/ x | |atan(x) 2*\/ x | |atan(x) 2*\/ x | 6*|------- + -------|*|------- - -------------- + ---------| |atan(x) 2*\/ x | 16*|------- - -------------- + ---------| ___ |atan(x) 2*\/ x | |atan(x) 2*\/ x | |
| | 2 3/2 / 2\ 5/2 3| | 3/2 ___ / 2\ 2| 12*|------- + -------| |------- + -------| 6*|------- + -------| 12*|------- + -------| | ___ 2| | 3/2 ___ / 2\ 2| 16*|------- + -------| | 3/2 ___ / 2\ 2| 32*\/ x *|------- + -------| 32*|------- + -------| |
_______________ | | / 2\ x *\1 + x / x / 2\ | | x \/ x *\1 + x / / 2\ | | ___ 2| | ___ 2| | ___ 2| | ___ 2| \ \/ x 1 + x / | x \/ x *\1 + x / / 2\ | | ___ 2| | x \/ x *\1 + x / / 2\ | | ___ 2| | ___ 2| |
/ ___ | \ \1 + x / \1 + x / / \ \1 + x / / \ \/ x 1 + x / \ \/ x 1 + x / \ \/ x 1 + x / \ \/ x 1 + x / \ \1 + x / / \ \/ x 1 + x / \ \1 + x / / \ \/ x 1 + x / \ \/ x 1 + x / |
\/ \/ x *atan(x) *|------------------------------------------------------- + ---------------------------------------- + ---------------------- + -------------------- - ---------------------- - ----------------------- - ------------------------------------------------------------ + ---------------------- + ----------------------------------------- + ---------------------------- + ------------------------|
| ___ 3/2 5/2 3/2 2 2 / 2\ 2 x*atan(x) 3/2 / 2\ ___ / 2\ 2 2 |
| \/ x x x x *atan (x) x *atan(x) x*\1 + x /*atan (x) x *\1 + x /*atan(x) \/ x *\1 + x /*atan(x) / 2\ ___ / 2\ 2 |
\ \1 + x / *atan(x) \/ x *\1 + x / *atan (x)/
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
64*atan(x)
$$\frac{\sqrt{\sqrt{x} \operatorname{atan}{\left(x \right)}} \left(\frac{32 \sqrt{x} \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} - \frac{6 \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \left(\frac{8 x^{\frac{3}{2}}}{\left(x^{2} + 1\right)^{2}} - \frac{4}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{x^{\frac{3}{2}}}\right)}{x \operatorname{atan}{\left(x \right)}} - \frac{12 \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)^{2}}{x \left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}} - \frac{6 \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)^{2}}{x^{2} \operatorname{atan}{\left(x \right)}} + \frac{4 \left(\frac{64 x^{\frac{5}{2}}}{\left(x^{2} + 1\right)^{3}} - \frac{40 \sqrt{x}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 \operatorname{atan}{\left(x \right)}}{x^{\frac{5}{2}}}\right)}{\sqrt{x}} + \frac{16 \left(\frac{8 x^{\frac{3}{2}}}{\left(x^{2} + 1\right)^{2}} - \frac{4}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{x^{\frac{3}{2}}}\right)}{\sqrt{x} \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{32 \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)}{\sqrt{x} \left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)^{3}}{x^{\frac{3}{2}} \operatorname{atan}^{2}{\left(x \right)}} + \frac{8 \left(\frac{8 x^{\frac{3}{2}}}{\left(x^{2} + 1\right)^{2}} - \frac{4}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{x^{\frac{3}{2}}}\right)}{x^{\frac{3}{2}}} + \frac{16 \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)}{x^{\frac{3}{2}} \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{12 \left(\frac{2 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right)}{x^{\frac{5}{2}}}\right)}{64 \operatorname{atan}{\left(x \right)}}$$
Gráfico