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 1/(x+1)^2
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Derivada de x^12
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Derivada de (x+3)/(x-2)
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Derivada de (x^3-4)
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Expresiones idénticas
- y=sqrt(arctg^ cuatro)*e^x/ln(3x)
- y es igual a raíz cuadrada de (arctg en el grado 4) multiplicar por e en el grado x dividir por ln(3x)
- y es igual a raíz cuadrada de (arctg en el grado cuatro) multiplicar por e en el grado x dividir por ln(3x)
- y=√(arctg^4)*e^x/ln(3x)
- y=sqrt(arctg4)*ex/ln(3x)
- y=sqrtarctg4*ex/ln3x
- y=sqrt(arctg⁴)*e^x/ln(3x)
- y=sqrt(arctg^4)e^x/ln(3x)
- y=sqrt(arctg4)ex/ln(3x)
- y=sqrtarctg4ex/ln3x
- y=sqrtarctg^4e^x/ln3x
- y=sqrt(arctg^4)*e^x dividir por ln(3x)
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x)^2-2*x
- sqrt(2-x^2)
- sqrt(x-1)/(sqrt(x^2)-x-1)
- sqrt(x)/(x+1)
- sqrt(x²+3x)
- arctg
- arctg^3*4x*3^sinx
- arctg(sqrt(x))
- arctg(cos(x))
- arctg(x+cosx)
- arctg^2(1/x)
- ln
- ln(x)+x
- ln(x+4)^11
- ln(x)+1
- ln(2x)/x
- ln|x|
Derivada de y=sqrt(arctg^4)*e^x/ln(3x)
Solución
Ha introducido
[src]
__________
/ 4 x
\/ atan (x) *E
----------------
log(3*x)
$$\frac{e^{x} \sqrt{\operatorname{atan}^{4}{\left(x \right)}}}{\log{\left(3 x \right)}}$$
(sqrt(atan(x)^4)*E^x)/log(3*x)
Primera derivada
[src]
x
2 x 2*atan(x)*e
atan (x)*e + ------------
2 2 x
1 + x atan (x)*e
-------------------------- - -----------
log(3*x) 2
x*log (3*x)
$$\frac{e^{x} \operatorname{atan}^{2}{\left(x \right)} + \frac{2 e^{x} \operatorname{atan}{\left(x \right)}}{x^{2} + 1}}{\log{\left(3 x \right)}} - \frac{e^{x} \operatorname{atan}^{2}{\left(x \right)}}{x \log{\left(3 x \right)}^{2}}$$
Segunda derivada
[src]
/ / 2 \ \
| 2 / 2 \ 2*|------ + atan(x)|*atan(x)|
| atan (x)*|1 + --------| | 2 | |
| 2 2*(-1 + 2*x*atan(x)) 4*atan(x) \ log(3*x)/ \1 + x / | x
|atan (x) - -------------------- + --------- + ----------------------- - ----------------------------|*e
| 2 2 2 x*log(3*x) |
| / 2\ 1 + x x *log(3*x) |
\ \1 + x / /
---------------------------------------------------------------------------------------------------------
log(3*x)
$$\frac{\left(\operatorname{atan}^{2}{\left(x \right)} + \frac{4 \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{2 \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(\operatorname{atan}{\left(x \right)} + \frac{2}{x^{2} + 1}\right) \operatorname{atan}{\left(x \right)}}{x \log{\left(3 x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(3 x \right)}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{2} \log{\left(3 x \right)}}\right) e^{x}}{\log{\left(3 x \right)}}$$
Tercera derivada
[src]
/ / 2 \ / 2 2*(-1 + 2*x*atan(x)) 4*atan(x)\ \
| | 3*x 4*x *atan(x) | 3*|atan (x) - -------------------- + ---------| 2 / 3 3 \ / 2 \ / 2 \ |
| 4*|------ - ------------ + atan(x)| | 2 2 | 2*atan (x)*|1 + -------- + ---------| 3*|1 + --------|*|------ + atan(x)|*atan(x)|
| | 2 2 | | / 2\ 1 + x | | log(3*x) 2 | \ log(3*x)/ | 2 | |
| 2 6*(-1 + 2*x*atan(x)) \1 + x 1 + x / 6*atan(x) \ \1 + x / / \ log (3*x)/ \1 + x / | x
|atan (x) - -------------------- - ----------------------------------- + --------- - ----------------------------------------------- - ------------------------------------- + -------------------------------------------|*e
| 2 2 2 x*log(3*x) 3 2 |
| / 2\ / 2\ 1 + x x *log(3*x) x *log(3*x) |
\ \1 + x / \1 + x / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(3*x)
$$\frac{\left(\operatorname{atan}^{2}{\left(x \right)} + \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{6 \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(\operatorname{atan}^{2}{\left(x \right)} + \frac{4 \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{2 \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}}\right)}{x \log{\left(3 x \right)}} + \frac{3 \left(1 + \frac{2}{\log{\left(3 x \right)}}\right) \left(\operatorname{atan}{\left(x \right)} + \frac{2}{x^{2} + 1}\right) \operatorname{atan}{\left(x \right)}}{x^{2} \log{\left(3 x \right)}} - \frac{2 \left(1 + \frac{3}{\log{\left(3 x \right)}} + \frac{3}{\log{\left(3 x \right)}^{2}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{3} \log{\left(3 x \right)}}\right) e^{x}}{\log{\left(3 x \right)}}$$
Gráfico