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^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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Expresiones idénticas
- y=(arctg*x-arcsin*x)/(tg*x-sin*x)
- y es igual a (arctg multiplicar por x menos arc seno de multiplicar por x) dividir por (tg multiplicar por x menos seno de multiplicar por x)
- y=(arctgx-arcsinx)/(tgx-sinx)
- y=arctgx-arcsinx/tgx-sinx
- y=(arctg*x-arcsin*x) dividir por (tg*x-sin*x)
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Expresiones semejantes
- y=(arctg*x-arcsin*x)/(tg*x+sin*x)
- y=(arctg*x+arcsin*x)/(tg*x-sin*x)
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Expresiones con funciones
- Seno sin
- sin(x+π)
- sin(7*x)^(2)
- sin(3*y)
- sin(2*x-pi/3)
- sin^-1(cosx)
Derivada de y=(arctg*x-arcsin*x)/(tg*x-sin*x)
Solución
Ha introducido
[src]
atan(x) - asin(x) ----------------- tan(x) - sin(x)
$$\frac{- \operatorname{asin}{\left(x \right)} + \operatorname{atan}{\left(x \right)}}{- \sin{\left(x \right)} + \tan{\left(x \right)}}$$
(atan(x) - asin(x))/(tan(x) - sin(x))
Primera derivada
[src]
1 1
------ - -----------
2 ________
1 + x / 2 / 2 \
\/ 1 - x (atan(x) - asin(x))*\-1 - tan (x) + cos(x)/
-------------------- + -------------------------------------------
tan(x) - sin(x) 2
(tan(x) - sin(x))
$$\frac{\frac{1}{x^{2} + 1} - \frac{1}{\sqrt{1 - x^{2}}}}{- \sin{\left(x \right)} + \tan{\left(x \right)}} + \frac{\left(- \operatorname{asin}{\left(x \right)} + \operatorname{atan}{\left(x \right)}\right) \left(\cos{\left(x \right)} - \tan^{2}{\left(x \right)} - 1\right)}{\left(- \sin{\left(x \right)} + \tan{\left(x \right)}\right)^{2}}$$
Segunda derivada
[src]
/ 2 \ / 1 1 \ / 2 \
| / 2 \ | 2*|------ - -----------|*\1 + tan (x) - cos(x)/
|2*\1 + tan (x) - cos(x)/ / 2 \ | | 2 ________|
(-atan(x) + asin(x))*|------------------------- + 2*\1 + tan (x)/*tan(x) + sin(x)| |1 + x / 2 |
/ 1 2 \ \ -tan(x) + sin(x) / \ \/ 1 - x /
x*|----------- + ---------| + ---------------------------------------------------------------------------------- - -----------------------------------------------
| 3/2 2| -tan(x) + sin(x) -tan(x) + sin(x)
|/ 2\ / 2\ |
\\1 - x / \1 + x / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------
-tan(x) + sin(x)
$$\frac{x \left(\frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) - \frac{2 \left(\frac{1}{x^{2} + 1} - \frac{1}{\sqrt{1 - x^{2}}}\right) \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} + \frac{\left(\operatorname{asin}{\left(x \right)} - \operatorname{atan}{\left(x \right)}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \sin{\left(x \right)} + \frac{2 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)^{2}}{\sin{\left(x \right)} - \tan{\left(x \right)}}\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}}}{\sin{\left(x \right)} - \tan{\left(x \right)}}$$
Tercera derivada
[src]
/ 2 \
/ 3 \ | / 2 \ |
| 2 / 2 \ / / 2 \ \ / 2 \ | / 1 1 \ |2*\1 + tan (x) - cos(x)/ / 2 \ | / 1 2 \ / 2 \
| / 2 \ 2 / 2 \ 6*\1 + tan (x) - cos(x)/ 6*\2*\1 + tan (x)/*tan(x) + sin(x)/*\1 + tan (x) - cos(x)/ | 3*|------ - -----------|*|------------------------- + 2*\1 + tan (x)/*tan(x) + sin(x)| 3*x*|----------- + ---------|*\1 + tan (x) - cos(x)/
(-atan(x) + asin(x))*|2*\1 + tan (x)/ + 4*tan (x)*\1 + tan (x)/ + ------------------------- + ---------------------------------------------------------- + cos(x)| | 2 ________| \ -tan(x) + sin(x) / | 3/2 2|
2 2 | 2 -tan(x) + sin(x) | |1 + x / 2 | |/ 2\ / 2\ |
1 2 8*x 3*x \ (-tan(x) + sin(x)) / \ \/ 1 - x / \\1 - x / \1 + x / /
----------- + --------- - --------- + ----------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- + ----------------------------------------------------
3/2 2 3 5/2 -tan(x) + sin(x) -tan(x) + sin(x) -tan(x) + sin(x)
/ 2\ / 2\ / 2\ / 2\
\1 - x / \1 + x / \1 + x / \1 - x /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
-tan(x) + sin(x)
$$\frac{- \frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} + \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x \left(\frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} - \frac{3 \left(\frac{1}{x^{2} + 1} - \frac{1}{\sqrt{1 - x^{2}}}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \sin{\left(x \right)} + \frac{2 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)^{2}}{\sin{\left(x \right)} - \tan{\left(x \right)}}\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} + \frac{\left(\operatorname{asin}{\left(x \right)} - \operatorname{atan}{\left(x \right)}\right) \left(\frac{6 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \sin{\left(x \right)}\right) \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \cos{\left(x \right)} + \frac{6 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)^{3}}{\left(\sin{\left(x \right)} - \tan{\left(x \right)}\right)^{2}}\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} + \frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{\sin{\left(x \right)} - \tan{\left(x \right)}}$$
Gráfico