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
-
¿Cómo usar?
- Derivada de:
-
Derivada de sin(2*x+3)
-
Derivada de (1-2*x)^3
-
Derivada de 5/x^4
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Derivada de x^3/x
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Expresiones idénticas
- y=ln(arctg2x)/x
- y es igual a ln(arctg2x) dividir por x
- y=lnarctg2x/x
- y=ln(arctg2x) dividir por x
-
Expresiones con funciones
- ln
- lnsin(x)
- ln(sin(2x+5))
- ln(x+e^x)
- ln(x/5)
- ln(e^(2*x)+1)
Derivada de y=ln(arctg2x)/x
Solución
Ha introducido
[src]
log(atan(2*x))
--------------
x
$$\frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x}$$
log(atan(2*x))/x
Primera derivada
[src]
log(atan(2*x)) 2
- -------------- + ----------------------
2 / 2\
x x*\1 + 4*x /*atan(2*x)
$$\frac{2}{x \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{2}}$$
Segunda derivada
[src]
/ / 1 \ \
| 2*|--------- + 4*x| |
|log(atan(2*x)) 2 \atan(2*x) / |
2*|-------------- - ---------------------- - ---------------------|
| 2 / 2\ 2 |
| x x*\1 + 4*x /*atan(2*x) / 2\ |
\ \1 + 4*x / *atan(2*x)/
-------------------------------------------------------------------
x
$$\frac{2 \left(- \frac{2 \left(4 x + \frac{1}{\operatorname{atan}{\left(2 x \right)}}\right)}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} - \frac{2}{x \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{2}}\right)}{x}$$
Tercera derivada
[src]
/ / 2 \ \
| | 1 16*x 6*x | |
| 8*|-1 + --------------------- + -------- + --------------------| / 1 \ |
| | / 2\ 2 2 / 2\ | 6*|--------- + 4*x| |
| 3*log(atan(2*x)) 6 \ \1 + 4*x /*atan (2*x) 1 + 4*x \1 + 4*x /*atan(2*x)/ \atan(2*x) / |
2*|- ---------------- + ----------------------- + ---------------------------------------------------------------- + -----------------------|
| 3 2 / 2\ 2 2 |
| x x *\1 + 4*x /*atan(2*x) / 2\ / 2\ |
\ \1 + 4*x / *atan(2*x) x*\1 + 4*x / *atan(2*x)/
---------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{2 \left(\frac{8 \left(\frac{16 x^{2}}{4 x^{2} + 1} + \frac{6 x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - 1 + \frac{1}{\left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}}\right)}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{6 \left(4 x + \frac{1}{\operatorname{atan}{\left(2 x \right)}}\right)}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{6}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{3 \log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{3}}\right)}{x}$$
Gráfico