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:
-
Derivada de (-4)/x^2
-
Derivada de 2/x²
-
Derivada de -2*y
-
Derivada de 3/2x
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Expresiones idénticas
- y=(arctgln^3x)^ cinco
- y es igual a (arctgln al cubo x) en el grado 5
- y es igual a (arctgln al cubo x) en el grado cinco
- y=(arctgln3x)5
- y=arctgln3x5
- y=(arctgln³x)⁵
- y=(arctgln en el grado 3x) en el grado 5
- y=arctgln^3x^5
Derivada de y=(arctgln^3x)^5
Solución
Ha introducido
[src]
5 / 3 \ \atan(x)*log (x)/
$$\left(\log{\left(x \right)}^{3} \operatorname{atan}{\left(x \right)}\right)^{5}$$
(atan(x)*log(x)^3)^5
Primera derivada
[src]
/ 3 2 \
5 15 |5*log (x) 15*log (x)*atan(x)|
atan (x)*log (x)*|--------- + ------------------|
| 2 x |
\ 1 + x /
--------------------------------------------------
3
atan(x)*log (x)
$$\frac{\log{\left(x \right)}^{15} \operatorname{atan}^{5}{\left(x \right)} \left(\frac{5 \log{\left(x \right)}^{3}}{x^{2} + 1} + \frac{15 \log{\left(x \right)}^{2} \operatorname{atan}{\left(x \right)}}{x}\right)}{\log{\left(x \right)}^{3} \operatorname{atan}{\left(x \right)}}$$
Segunda derivada
[src]
/ /log(x) 3*atan(x)\ /log(x) 3*atan(x)\ \
| |------ + ---------|*log(x) 3*|------ + ---------|*atan(x)|
| 2 / 2 \ | 2 x | | 2 x | |
3 13 | /log(x) 3*atan(x)\ | 6*atan(x) 6*log(x) 2*x*log (x) 3*atan(x)*log(x)| \1 + x / \1 + x / |
5*atan (x)*log (x)*|5*|------ + ---------| - |- --------- - ---------- + ----------- + ----------------|*atan(x) - --------------------------- - ------------------------------|
| | 2 x | | 2 / 2\ 2 2 | 2 x |
| \1 + x / | x x*\1 + x / / 2\ x | 1 + x |
\ \ \1 + x / / /
$$5 \left(5 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right)^{2} - \left(\frac{2 x \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \log{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{3 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2}}\right) \operatorname{atan}{\left(x \right)} - \frac{\left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \log{\left(x \right)}}{x^{2} + 1} - \frac{3 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \operatorname{atan}{\left(x \right)}}{x}\right) \log{\left(x \right)}^{13} \operatorname{atan}^{3}{\left(x \right)}$$
Tercera derivada
[src]
/ / 2 \ / 2 \ \
| 2 2 | 6*atan(x) 6*log(x) 2*x*log (x) 3*atan(x)*log(x)| 2 | 6*atan(x) 6*log(x) 2*x*log (x) 3*atan(x)*log(x)| |
| 2 /log(x) 3*atan(x)\ /log(x) 3*atan(x)\ 9*atan (x)*|- --------- - ---------- + ----------- + ----------------| /log(x) 3*atan(x)\ 2 /log(x) 3*atan(x)\ 3*|- --------- - ---------- + ----------- + ----------------|*atan(x)*log(x) 2 /log(x) 3*atan(x)\ /log(x) 3*atan(x)\ 2 /log(x) 3*atan(x)\ |
| 33*atan (x)*|------ + ---------| 15*|------ + ---------| *atan(x) | 2 / 2\ 2 2 | 5*|------ + ---------| *log(x) 3*log (x)*|------ + ---------| | 2 / 2\ 2 2 | 3*atan (x)*|------ + ---------|*log(x) 24*|------ + ---------|*atan(x)*log(x) 2*x*log (x)*|------ + ---------|*atan(x)|
| / 2 3 2 2 2 3 \ / 2 2 2 2 \ | 2 x | | 2 x | | x x*\1 + x / / 2\ x | | 2 x | / 2 \ | 2 x | | x x*\1 + x / / 2\ x | | 2 x | | 2 x | | 2 x | |
2 12 | 2 | 18*log (x) 2*log (x) 6*atan(x) 18*atan(x)*log(x) 9*log (x) 6*log (x)*atan(x) 8*x *log (x) 18*log(x) | /log(x) 3*atan(x)\ |4*log (x) 42*atan (x) 3*atan (x)*log(x) 2*x*log (x)*atan(x) 30*atan(x)*log(x)| \1 + x / \1 + x / \ \1 + x / / \1 + x / /log(x) 3*atan(x)\ | 6*atan(x) 6*log(x) 2*x*log (x) 3*atan(x)*log(x)| \1 + x / \ \1 + x / / \1 + x / \1 + x / \1 + x / |
5*atan (x)*log (x)*|atan (x)*|- ---------- - --------- + --------- - ----------------- - ----------- + ----------------- + ------------ + -----------| + 5*|------ + ---------|*|--------- + ----------- - ----------------- - ------------------- + -----------------| - -------------------------------- - -------------------------------- - ---------------------------------------------------------------------- - ------------------------------ - 5*|------ + ---------|*|- --------- - ---------- + ----------- + ----------------|*atan(x) - ------------------------------ - ---------------------------------------------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------------|
| | 2 2 3 3 2 / 2\ 3 3 2 / 2\| | 2 x | | 2 2 2 2 / 2\ | 2 x x 2 | 2 x | | 2 / 2\ 2 2 | 2 2 2 / 2\ 2 |
| | / 2\ / 2\ x x x *\1 + x / x / 2\ x *\1 + x /| \1 + x / |/ 2\ x x / 2\ x*\1 + x / | x 1 + x \1 + x / | x x*\1 + x / / 2\ x | / 2\ 1 + x x x*\1 + x / / 2\ |
\ \ \1 + x / \1 + x / \1 + x / / \\1 + x / \1 + x / / \ \1 + x / / \1 + x / \1 + x / /
$$5 \left(\frac{2 x \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \log{\left(x \right)}^{2} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - 5 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \left(\frac{2 x \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \log{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{3 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2}}\right) \operatorname{atan}{\left(x \right)} + 5 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \left(- \frac{2 x \log{\left(x \right)}^{2} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{4 \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{30 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} - \frac{3 \log{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2}} + \frac{42 \operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) + \left(\frac{8 x^{2} \log{\left(x \right)}^{3}}{\left(x^{2} + 1\right)^{3}} - \frac{2 \log{\left(x \right)}^{3}}{\left(x^{2} + 1\right)^{2}} - \frac{18 \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{9 \log{\left(x \right)}^{2}}{x^{2} \left(x^{2} + 1\right)} + \frac{18 \log{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{6 \log{\left(x \right)}^{2} \operatorname{atan}{\left(x \right)}}{x^{3}} - \frac{18 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{3}} + \frac{6 \operatorname{atan}{\left(x \right)}}{x^{3}}\right) \operatorname{atan}^{2}{\left(x \right)} - \frac{5 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)}}{x^{2} + 1} - \frac{3 \left(\frac{2 x \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \log{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{3 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{3 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{15 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right)^{2} \operatorname{atan}{\left(x \right)}}{x} - \frac{9 \left(\frac{2 x \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \log{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{3 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x} - \frac{24 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{3 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \log{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2}} - \frac{33 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{3 \operatorname{atan}{\left(x \right)}}{x}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)}^{12} \operatorname{atan}^{2}{\left(x \right)}$$
Gráfico