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^4(3x-7)^5
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Derivada de x⁴+8x²+8
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Derivada de (x^3+e^x)/sqrt(4-9*x^5)
- Derivada de x=3acost-acos3t,y=3asint-asin3tfinddy÷dx
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Expresiones idénticas
- y=arctg((√x)/(dos +(√(uno -x^ dos)^(uno / tres))))
- y es igual a arctg((√x) dividir por (2 más (√(1 menos x al cuadrado ) en el grado (1 dividir por 3))))
- y es igual a arctg((√x) dividir por (dos más (√(uno menos x en el grado dos) en el grado (uno dividir por tres))))
- y=arctg((√x)/(2+(√(1-x2)(1/3))))
- y=arctg√x/2+√1-x21/3
- y=arctg((√x)/(2+(√(1-x²)^(1/3))))
- y=arctg((√x)/(2+(√(1-x en el grado 2) en el grado (1/3))))
- y=arctg√x/2+√1-x^2^1/3
- y=arctg((√x) dividir por (2+(√(1-x^2)^(1 dividir por 3))))
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Expresiones semejantes
- y=arctg((√x)/(2+(√(1+x^2)^(1/3))))
- y=arctg((√x)/(2-(√(1-x^2)^(1/3))))
Derivada de y=arctg((√x)/(2+(√(1-x^2)^(1/3))))
Solución
Ha introducido
[src]
/ ___ \
| \/ x |
atan|---------------------|
| _____________|
| / ________ |
| 3 / / 2 |
\2 + \/ \/ 1 - x /
$$\operatorname{atan}{\left(\frac{\sqrt{x}}{\sqrt[3]{\sqrt{1 - x^{2}}} + 2} \right)}$$
atan(sqrt(x)/(2 + (sqrt(1 - x^2))^(1/3)))
Primera derivada
[src]
3/2
1 x
------------------------------- + --------------------------------------
/ _____________\ 2
| / ________ | / _____________\
___ | 3 / / 2 | 5/6 | / ________ |
2*\/ x *\2 + \/ \/ 1 - x / / 2\ | 3 / / 2 |
3*\1 - x / *\2 + \/ \/ 1 - x /
------------------------------------------------------------------------
x
1 + ------------------------
2
/ _____________\
| / ________ |
| 3 / / 2 |
\2 + \/ \/ 1 - x /
$$\frac{\frac{x^{\frac{3}{2}}}{3 \left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[3]{\sqrt{1 - x^{2}}} + 2\right)^{2}} + \frac{1}{2 \sqrt{x} \left(\sqrt[3]{\sqrt{1 - x^{2}}} + 2\right)}}{\frac{x}{\left(\sqrt[3]{\sqrt{1 - x^{2}}} + 2\right)^{2}} + 1}$$
Segunda derivada
[src]
/ 2 \ / 3/2 \
| 2*x | | 3 2*x |
2*|3 + -----------------------------|*|----- + -----------------------------|
| 5/6 / ________\| | ___ 5/6 / ________\|
5/2 5/2 ___ | / 2\ | 6 / 2 || |\/ x / 2\ | 6 / 2 ||
9 8*x 20*x 24*\/ x \ \1 - x / *\2 + \/ 1 - x // \ \1 - x / *\2 + \/ 1 - x //
- ---- + ------------------------------ + ------------------------------ + ----------------------------- - -----------------------------------------------------------------------------
3/2 2 11/6 / ________\ 5/6 / ________\ 2
x 5/3 / ________\ / 2\ | 6 / 2 | / 2\ | 6 / 2 | / ________\
/ 2\ | 6 / 2 | \1 - x / *\2 + \/ 1 - x / \1 - x / *\2 + \/ 1 - x / / x \ | 6 / 2 |
\1 - x / *\2 + \/ 1 - x / |1 + ------------------|*\2 + \/ 1 - x /
| 2|
| / ________\ |
| | 6 / 2 | |
\ \2 + \/ 1 - x / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ________\
/ x \ | 6 / 2 |
36*|1 + ------------------|*\2 + \/ 1 - x /
| 2|
| / ________\ |
| | 6 / 2 | |
\ \2 + \/ 1 - x / /
$$\frac{\frac{8 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{20 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{11}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{24 \sqrt{x}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} - \frac{2 \left(\frac{2 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{3}{\sqrt{x}}\right) \left(\frac{2 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + 3\right)}{\left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} - \frac{9}{x^{\frac{3}{2}}}}{36 \left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)}$$
Tercera derivada
[src]
/ 2 \ / 5/2 5/2 ___ \ 2
| 2*x | | 9 8*x 20*x 24*\/ x | / 2 \ / 3/2 \ / 3/2 \ / 2 2 \
|3 + -----------------------------|*|- ---- + ------------------------------ + ------------------------------ + -----------------------------| | 2*x | | 3 2*x | | 3 2*x | | 9 5*x 3*x |
| 5/6 / ________\| | 3/2 2 11/6 / ________\ 5/6 / ________\| |3 + -----------------------------| *|----- + -----------------------------| x*|----- + -----------------------------|*|----------- + ------------ + -----------------------------|
| / 2\ | 6 / 2 || | x 5/3 / ________\ / 2\ | 6 / 2 | / 2\ | 6 / 2 || | 5/6 / ________\| | ___ 5/6 / ________\| | ___ 5/6 / ________\| | 5/6 11/6 5/3 / ________\|
3/2 7/2 3/2 7/2 7/2 \ \1 - x / *\2 + \/ 1 - x // | / 2\ | 6 / 2 | \1 - x / *\2 + \/ 1 - x / \1 - x / *\2 + \/ 1 - x /| | / 2\ | 6 / 2 || |\/ x / 2\ | 6 / 2 || |\/ x / 2\ | 6 / 2 || |/ 2\ / 2\ / 2\ | 6 / 2 ||
3 x 1 2*x 5*x 10*x 55*x \ \1 - x / *\2 + \/ 1 - x / / \ \1 - x / *\2 + \/ 1 - x // \ \1 - x / *\2 + \/ 1 - x // \ \1 - x / *\2 + \/ 1 - x // \\1 - x / \1 - x / \1 - x / *\2 + \/ 1 - x //
------ + ------------------------------ + ------------------------------------- + -------------------------------- + -------------------------------- + -------------------------------- + --------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
5/2 2 5/6 / ________\ 3 11/6 / ________\ 2 17/6 / ________\ 2 4 3
8*x 5/3 / ________\ ___ / 2\ | 6 / 2 | 5/2 / ________\ / 2\ | 6 / 2 | 8/3 / ________\ / 2\ | 6 / 2 | / ________\ 2 / ________\ / ________\
/ 2\ | 6 / 2 | 4*\/ x *\1 - x / *\2 + \/ 1 - x / / 2\ | 6 / 2 | 2*\1 - x / *\2 + \/ 1 - x / / 2\ | 6 / 2 | 27*\1 - x / *\2 + \/ 1 - x / / x \ | 6 / 2 | / x \ | 6 / 2 | / x \ | 6 / 2 |
\1 - x / *\2 + \/ 1 - x / 9*\1 - x / *\2 + \/ 1 - x / 9*\1 - x / *\2 + \/ 1 - x / 54*|1 + ------------------|*\2 + \/ 1 - x / 27*|1 + ------------------| *\2 + \/ 1 - x / 27*|1 + ------------------|*\2 + \/ 1 - x /
| 2| | 2| | 2|
| / ________\ | | / ________\ | | / ________\ |
| | 6 / 2 | | | | 6 / 2 | | | | 6 / 2 | |
\ \2 + \/ 1 - x / / \ \2 + \/ 1 - x / / \ \2 + \/ 1 - x / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ________\
/ x \ | 6 / 2 |
|1 + ------------------|*\2 + \/ 1 - x /
| 2|
| / ________\ |
| | 6 / 2 | |
\ \2 + \/ 1 - x / /
$$\frac{\frac{2 x^{\frac{7}{2}}}{9 \left(1 - x^{2}\right)^{\frac{5}{2}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{3}} + \frac{10 x^{\frac{7}{2}}}{9 \left(1 - x^{2}\right)^{\frac{8}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{55 x^{\frac{7}{2}}}{27 \left(1 - x^{2}\right)^{\frac{17}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{5 x^{\frac{3}{2}}}{2 \left(1 - x^{2}\right)^{\frac{11}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} - \frac{x \left(\frac{2 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{3}{\sqrt{x}}\right) \left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{5 x^{2}}{\left(1 - x^{2}\right)^{\frac{11}{6}}} + \frac{9}{\left(1 - x^{2}\right)^{\frac{5}{6}}}\right)}{27 \left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)^{3}} - \frac{\left(\frac{2 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + 3\right) \left(\frac{8 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{3}} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{20 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{11}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{24 \sqrt{x}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} - \frac{9}{x^{\frac{3}{2}}}\right)}{54 \left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + \frac{\left(\frac{2 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{3}{\sqrt{x}}\right) \left(\frac{2 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + 3\right)^{2}}{27 \left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right)^{2} \left(\sqrt[6]{1 - x^{2}} + 2\right)^{4}} + \frac{1}{4 \sqrt{x} \left(1 - x^{2}\right)^{\frac{5}{6}} \left(\sqrt[6]{1 - x^{2}} + 2\right)} + \frac{3}{8 x^{\frac{5}{2}}}}{\left(\frac{x}{\left(\sqrt[6]{1 - x^{2}} + 2\right)^{2}} + 1\right) \left(\sqrt[6]{1 - x^{2}} + 2\right)}$$
Gráfico