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^(7/6)
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Derivada de x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Expresiones idénticas
- x/(x^ dos *tgx)
- x dividir por (x al cuadrado multiplicar por tgx)
- x dividir por (x en el grado dos multiplicar por tgx)
- x/(x2*tgx)
- x/x2*tgx
- x/(x²*tgx)
- x/(x en el grado 2*tgx)
- x/(x^2tgx)
- x/(x2tgx)
- x/x2tgx
- x/x^2tgx
- x dividir por (x^2*tgx)
Derivada de x/(x^2*tgx)
Solución
Ha introducido
[src]
x --------- 2 x *tan(x)
$$\frac{x}{x^{2} \tan{\left(x \right)}}$$
x/((x^2*tan(x)))
Solución detallada
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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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Según el principio, aplicamos: tenemos
Para calcular :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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Según el principio, aplicamos: tenemos
; calculamos :
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Reescribimos las funciones para diferenciar:
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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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La derivada del seno es igual al coseno:
Para calcular :
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La derivada del coseno es igual a menos el seno:
Ahora aplicamos la regla de la derivada de una divesión:
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Como resultado de:
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Ahora aplicamos la regla de la derivada de una divesión:
Simplificamos:
Respuesta:
Primera derivada
[src]
2 / 2 \
1 - x *\1 + tan (x)/ - 2*x*tan(x)
--------- + -------------------------------
2 3 2
x *tan(x) x *tan (x)
$$\frac{1}{x^{2} \tan{\left(x \right)}} + \frac{- x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) - 2 x \tan{\left(x \right)}}{x^{3} \tan^{2}{\left(x \right)}}$$
Segunda derivada
[src]
/ 2 \ / / 2 \ 2 / 2 \ \ / 2 \ / / 2 \\
|2 1 + tan (x)| / / 2 \\ 2*\2*x*\1 + tan (x)/ + x *\1 + tan (x)/*tan(x) + tan(x)/ \1 + tan (x)/*\2*tan(x) + x*\1 + tan (x)//
|- + -----------|*\2*tan(x) + x*\1 + tan (x)// - -------------------------------------------------------- + ------------------------------------------
\x tan(x) / x tan(x)
------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
x *tan (x)
$$\frac{\left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \frac{2}{x}\right) + \frac{\left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{2 \left(x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right)}{x}}{x^{2} \tan^{2}{\left(x \right)}}$$
Tercera derivada
[src]
// 2 \ / / 2 \ 2 / 2 \ \ / / 2 \\ / 2 \ / / 2 \\\ / 2 \ / 2 \ / 2 \
/ 2 \ / 2 \ ||2 1 + tan (x)| / / 2 \\ 2*\2*x*\1 + tan (x)/ + x *\1 + tan (x)/*tan(x) + tan(x)/ 2*\2*tan(x) + x*\1 + tan (x)// \1 + tan (x)/*\2*tan(x) + x*\1 + tan (x)//| 2 |2 1 + tan (x)| / / 2 \\ |2 1 + tan (x)| / / 2 \ 2 / 2 \ \ / 2 \ |2 1 + tan (x)| / / 2 \\
/ / 2 \\ | 2 2 / 2 \ 2 2 / 2 \ / 2 \ | | / 2 \ / 2 \| 3*||- + -----------|*\2*tan(x) + x*\1 + tan (x)// - -------------------------------------------------------- + ------------------------------ + ------------------------------------------| / / 2 \ 2 / 2 \ \ / 2 \ / / 2 \\ 2*|- + -----------|*\2*tan(x) + x*\1 + tan (x)// 2*|- + -----------|*\2*x*\1 + tan (x)/ + x *\1 + tan (x)/*tan(x) + tan(x)/ \1 + tan (x)/*|- + -----------|*\2*tan(x) + x*\1 + tan (x)// / 2 \ / / 2 \\ / 2 \ / / 2 \ 2 / 2 \ \
10*\2*tan(x) + x*\1 + tan (x)// 2*\3 + 3*tan (x) + x *\1 + tan (x)/ + 2*x *tan (x)*\1 + tan (x)/ + 6*x*\1 + tan (x)/*tan(x)/ / / 2 \\ | 2 3 \1 + tan (x)/ 2*\1 + tan (x)/| / 2 \ / / 2 \\ \\x tan(x) / x x tan(x) / 12*\2*x*\1 + tan (x)/ + x *\1 + tan (x)/*tan(x) + tan(x)/ 3*\1 + tan (x)/ *\2*tan(x) + x*\1 + tan (x)// \x tan(x) / \x tan(x) / \x tan(x) / 8*\1 + tan (x)/*\2*tan(x) + x*\1 + tan (x)// 6*\1 + tan (x)/*\2*x*\1 + tan (x)/ + x *\1 + tan (x)/*tan(x) + tan(x)/
- ------------------------------- - --------------------------------------------------------------------------------------------- - 2*\2*tan(x) + x*\1 + tan (x)//*|-1 - tan (x) + -- + -------------- + ---------------| + 2*\1 + tan (x)/*\2*tan(x) + x*\1 + tan (x)// + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- - --------------------------------------------- - ------------------------------------------------ + -------------------------------------------------------------------------- - ------------------------------------------------------------ - -------------------------------------------- + ----------------------------------------------------------------------
2 x | 2 2 x*tan(x) | x 2 2 x x tan(x) x*tan(x) x*tan(x)
x \ x tan (x) / x tan (x)
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
x *tan (x)
$$\frac{- \frac{\left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \frac{2}{x}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{3 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) - 2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} - \tan^{2}{\left(x \right)} - 1 + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} + \frac{3}{x^{2}}\right) - \frac{2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \frac{2}{x}\right)}{x} - \frac{8 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} + \frac{2 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \frac{2}{x}\right) \left(x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right)}{x} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right)}{x \tan{\left(x \right)}} + \frac{3 \left(\left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \frac{2}{x}\right) + \frac{\left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \frac{2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right)}{x} - \frac{2 \left(x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right)}{x}\right)}{x} - \frac{2 \left(x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 6 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 3 \tan^{2}{\left(x \right)} + 3\right)}{x} - \frac{10 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 \tan{\left(x \right)}\right)}{x^{2}} + \frac{12 \left(x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right)}{x^{2}}}{x^{2} \tan^{2}{\left(x \right)}}$$
Gráfico