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 (x-1)/(x+1)
-
Derivada de -3/x
-
Derivada de x*x
-
Derivada de x/4
-
Expresiones idénticas
- y=ctg^ ocho (ln^ dos (8x))* cinco ^x^ dos
- y es igual a ctg en el grado 8(ln al cuadrado (8x)) multiplicar por 5 en el grado x al cuadrado
- y es igual a ctg en el grado ocho (ln en el grado dos (8x)) multiplicar por cinco en el grado x en el grado dos
- y=ctg8(ln2(8x))*5x2
- y=ctg8ln28x*5x2
- y=ctg⁸(ln²(8x))*5^x²
- y=ctg en el grado 8(ln en el grado 2(8x))*5 en el grado x en el grado 2
- y=ctg^8(ln^2(8x))5^x^2
- y=ctg8(ln2(8x))5x2
- y=ctg8ln28x5x2
- y=ctg^8ln^28x5^x^2
-
Expresiones con funciones
- ctg
- ctg(2x+1)
- ctg(x/7)
- ctg3x*arccos(3x)^2
- ctg(x^2)
- ln
- ln(x/2)
- ln((x^2)/(1-x^2))
- ln(e)
- ln^2x
- ln(x-3)
Derivada de y=ctg^8(ln^2(8x))*5^x^2
Solución
Ha introducido
[src]
/ 2\ 8/ 2 \ \x / cot \log (8*x)/*5
$$5^{x^{2}} \cot^{8}{\left(\log{\left(8 x \right)}^{2} \right)}$$
cot(log(8*x)^2)^8*5^(x^2)
Primera derivada
[src]
/ 2\
/ 2\ \x / 7/ 2 \ / 2/ 2 \\
\x / 8/ 2 \ 16*5 *cot \log (8*x)/*\-1 - cot \log (8*x)//*log(8*x)
2*x*5 *cot \log (8*x)/*log(5) + --------------------------------------------------------
x
$$2 \cdot 5^{x^{2}} x \log{\left(5 \right)} \cot^{8}{\left(\log{\left(8 x \right)}^{2} \right)} + \frac{16 \cdot 5^{x^{2}} \left(- \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} - 1\right) \log{\left(8 x \right)} \cot^{7}{\left(\log{\left(8 x \right)}^{2} \right)}}{x}$$
Segunda derivada
[src]
/ 2\ / / 2/ 2 \\ / / 2 \ / 2 \ 2/ 2 \ 2 2 / 2/ 2 \\\ \
\x / 6/ 2 \ | 2/ 2 \ / 2 \ 8*\1 + cot \log (8*x)//*\- cot\log (8*x)/ + cot\log (8*x)/*log(8*x) + 4*cot \log (8*x)/*log (8*x) + 14*log (8*x)*\1 + cot \log (8*x)/// / 2/ 2 \\ / 2 \ |
2*5 *cot \log (8*x)/*|cot \log (8*x)/*\1 + 2*x *log(5)/*log(5) + --------------------------------------------------------------------------------------------------------------------------------------- - 32*\1 + cot \log (8*x)//*cot\log (8*x)/*log(5)*log(8*x)|
| 2 |
\ x /
$$2 \cdot 5^{x^{2}} \left(\left(2 x^{2} \log{\left(5 \right)} + 1\right) \log{\left(5 \right)} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} - 32 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(5 \right)} \log{\left(8 x \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)} + \frac{8 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \left(14 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)}^{2} + 4 \log{\left(8 x \right)}^{2} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + \log{\left(8 x \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)} - \cot{\left(\log{\left(8 x \right)}^{2} \right)}\right)}{x^{2}}\right) \cot^{6}{\left(\log{\left(8 x \right)}^{2} \right)}$$
Tercera derivada
[src]
/ / 2 \ \
/ 2\ | / 2/ 2 \\ | 2/ 2 \ 3/ 2 \ 2/ 2 \ 3/ 2 \ 2 4/ 2 \ 3 / 2/ 2 \\ 3 / 2/ 2 \\ / 2 \ 2 / 2/ 2 \\ / 2 \ 2/ 2 \ 3 / 2/ 2 \\| / 2/ 2 \\ / / 2 \ / 2 \ 2/ 2 \ 2 2 / 2/ 2 \\\ / 2 \ 2/ 2 \ / 2/ 2 \\ / 2 \ |
\x / 5/ 2 \ | 4*\1 + cot \log (8*x)//*\- 3*cot \log (8*x)/ - 12*cot \log (8*x)/*log(8*x) + 2*cot \log (8*x)/*log(8*x) + 12*cot \log (8*x)/*log (8*x) + 16*cot \log (8*x)/*log (8*x) + 168*\1 + cot \log (8*x)// *log (8*x) - 42*\1 + cot \log (8*x)//*cot\log (8*x)/*log(8*x) + 42*log (8*x)*\1 + cot \log (8*x)//*cot\log (8*x)/ + 176*cot \log (8*x)/*log (8*x)*\1 + cot \log (8*x)/// 3/ 2 \ 2 / 2 \ 24*\1 + cot \log (8*x)//*\- cot\log (8*x)/ + cot\log (8*x)/*log(8*x) + 4*cot \log (8*x)/*log (8*x) + 14*log (8*x)*\1 + cot \log (8*x)///*cot\log (8*x)/*log(5) 24*cot \log (8*x)/*\1 + cot \log (8*x)//*\1 + 2*x *log(5)/*log(5)*log(8*x)|
4*5 *cot \log (8*x)/*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + x*cot \log (8*x)/*log (5)*\3 + 2*x *log(5)/ + -------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------|
| 3 x x |
\ x /
$$4 \cdot 5^{x^{2}} \left(x \left(2 x^{2} \log{\left(5 \right)} + 3\right) \log{\left(5 \right)}^{2} \cot^{3}{\left(\log{\left(8 x \right)}^{2} \right)} - \frac{24 \left(2 x^{2} \log{\left(5 \right)} + 1\right) \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(5 \right)} \log{\left(8 x \right)} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)}}{x} + \frac{24 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \left(14 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)}^{2} + 4 \log{\left(8 x \right)}^{2} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + \log{\left(8 x \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)} - \cot{\left(\log{\left(8 x \right)}^{2} \right)}\right) \log{\left(5 \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)}}{x} - \frac{4 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \left(168 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right)^{2} \log{\left(8 x \right)}^{3} + 176 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)}^{3} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 42 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)}^{2} \cot{\left(\log{\left(8 x \right)}^{2} \right)} - 42 \left(\cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} + 1\right) \log{\left(8 x \right)} \cot{\left(\log{\left(8 x \right)}^{2} \right)} + 16 \log{\left(8 x \right)}^{3} \cot^{4}{\left(\log{\left(8 x \right)}^{2} \right)} + 12 \log{\left(8 x \right)}^{2} \cot^{3}{\left(\log{\left(8 x \right)}^{2} \right)} - 12 \log{\left(8 x \right)} \cot^{3}{\left(\log{\left(8 x \right)}^{2} \right)} + 2 \log{\left(8 x \right)} \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)} - 3 \cot^{2}{\left(\log{\left(8 x \right)}^{2} \right)}\right)}{x^{3}}\right) \cot^{5}{\left(\log{\left(8 x \right)}^{2} \right)}$$
Gráfico