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 -2x
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Derivada de e^-1
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Derivada de y
- Derivada de x^e^x
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Expresiones idénticas
- xsin5x/(arctg^ dos (3x))
- x seno de 5x dividir por (arctg al cuadrado (3x))
- x seno de 5x dividir por (arctg en el grado dos (3x))
- xsin5x/(arctg2(3x))
- xsin5x/arctg23x
- xsin5x/(arctg²(3x))
- xsin5x/(arctg en el grado 2(3x))
- xsin5x/arctg^23x
- xsin5x dividir por (arctg^2(3x))
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Expresiones con funciones
- arctg
- arctg(sqrt(x))
- arctg(cos(x))
- arctg^2(1/x)
- arctg(x+cosx)
Derivada de xsin5x/(arctg^2(3x))
Solución
Ha introducido
[src]
x*sin(5*x)
----------
2
atan (3*x)
$$\frac{x \sin{\left(5 x \right)}}{\operatorname{atan}^{2}{\left(3 x \right)}}$$
(x*sin(5*x))/atan(3*x)^2
Primera derivada
[src]
5*x*cos(5*x) + sin(5*x) 6*x*sin(5*x)
----------------------- - ---------------------
2 / 2\ 3
atan (3*x) \1 + 9*x /*atan (3*x)
$$- \frac{6 x \sin{\left(5 x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}^{3}{\left(3 x \right)}} + \frac{5 x \cos{\left(5 x \right)} + \sin{\left(5 x \right)}}{\operatorname{atan}^{2}{\left(3 x \right)}}$$
Segunda derivada
[src]
/ 1 \
54*x*|--------- + 2*x|*sin(5*x)
12*(5*x*cos(5*x) + sin(5*x)) \atan(3*x) /
10*cos(5*x) - 25*x*sin(5*x) - ---------------------------- + -------------------------------
/ 2\ 2
\1 + 9*x /*atan(3*x) / 2\
\1 + 9*x / *atan(3*x)
--------------------------------------------------------------------------------------------
2
atan (3*x)
$$\frac{\frac{54 x \left(2 x + \frac{1}{\operatorname{atan}{\left(3 x \right)}}\right) \sin{\left(5 x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} - 25 x \sin{\left(5 x \right)} + 10 \cos{\left(5 x \right)} - \frac{12 \left(5 x \cos{\left(5 x \right)} + \sin{\left(5 x \right)}\right)}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}$$
Tercera derivada
[src]
/ 2 \
| 6 36*x 27*x |
/ 1 \ 108*x*|-1 + --------------------- + -------- + --------------------|*sin(5*x)
162*|--------- + 2*x|*(5*x*cos(5*x) + sin(5*x)) | / 2\ 2 2 / 2\ |
90*(-2*cos(5*x) + 5*x*sin(5*x)) \atan(3*x) / \ \1 + 9*x /*atan (3*x) 1 + 9*x \1 + 9*x /*atan(3*x)/
-75*sin(5*x) - 125*x*cos(5*x) + ------------------------------- + ----------------------------------------------- - -----------------------------------------------------------------------------
/ 2\ 2 2
\1 + 9*x /*atan(3*x) / 2\ / 2\
\1 + 9*x / *atan(3*x) \1 + 9*x / *atan(3*x)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
atan (3*x)
$$\frac{- 125 x \cos{\left(5 x \right)} - \frac{108 x \left(\frac{36 x^{2}}{9 x^{2} + 1} + \frac{27 x}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} - 1 + \frac{6}{\left(9 x^{2} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}\right) \sin{\left(5 x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + \frac{162 \left(2 x + \frac{1}{\operatorname{atan}{\left(3 x \right)}}\right) \left(5 x \cos{\left(5 x \right)} + \sin{\left(5 x \right)}\right)}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} - 75 \sin{\left(5 x \right)} + \frac{90 \left(5 x \sin{\left(5 x \right)} - 2 \cos{\left(5 x \right)}\right)}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}$$
Gráfico