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 x^-0,2
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Derivada de e-x
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Derivada de e^e
- Derivada de e^((3*x)^2)
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Expresiones idénticas
- (x+x^ siete)^ctg(3x)
- (x más x en el grado 7) en el grado ctg(3x)
- (x más x en el grado siete) en el grado ctg(3x)
- (x+x7)ctg(3x)
- x+x7ctg3x
- (x+x⁷)^ctg(3x)
- x+x^7^ctg3x
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Expresiones semejantes
- (x-x^7)^ctg(3x)
Derivada de (x+x^7)^ctg(3x)
Solución
Ha introducido
[src]
cot(3*x) / 7\ \x + x /
$$\left(x^{7} + x\right)^{\cot{\left(3 x \right)}}$$
(x + x^7)^cot(3*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
cot(3*x) / / 6\ \
/ 7\ |/ 2 \ / 7\ \1 + 7*x /*cot(3*x)|
\x + x / *|\-3 - 3*cot (3*x)/*log\x + x / + -------------------|
| 7 |
\ x + x /
$$\left(x^{7} + x\right)^{\cot{\left(3 x \right)}} \left(\frac{\left(7 x^{6} + 1\right) \cot{\left(3 x \right)}}{x^{7} + x} + \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) \log{\left(x^{7} + x \right)}\right)$$
Segunda derivada
[src]
/ 2 2 \
cot(3*x) |/ / 6\ \ 4 / 6\ / 2 \ / 6\|
/ / 6\\ || / 2 \ / / 6\\ \1 + 7*x /*cot(3*x)| / 2 \ / / 6\\ 42*x *cot(3*x) \1 + 7*x / *cot(3*x) 6*\1 + cot (3*x)/*\1 + 7*x /|
\x*\1 + x // *||- 3*\1 + cot (3*x)/*log\x*\1 + x // + -------------------| + 18*\1 + cot (3*x)/*cot(3*x)*log\x*\1 + x // + -------------- - -------------------- - ----------------------------|
|| / 6\ | 6 2 / 6\ |
|\ x*\1 + x / / 1 + x 2 / 6\ x*\1 + x / |
\ x *\1 + x / /
$$\left(x \left(x^{6} + 1\right)\right)^{\cot{\left(3 x \right)}} \left(\frac{42 x^{4} \cot{\left(3 x \right)}}{x^{6} + 1} + \left(- 3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(x \left(x^{6} + 1\right) \right)} + \frac{\left(7 x^{6} + 1\right) \cot{\left(3 x \right)}}{x \left(x^{6} + 1\right)}\right)^{2} + 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(x \left(x^{6} + 1\right) \right)} \cot{\left(3 x \right)} - \frac{6 \left(7 x^{6} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x \left(x^{6} + 1\right)} - \frac{\left(7 x^{6} + 1\right)^{2} \cot{\left(3 x \right)}}{x^{2} \left(x^{6} + 1\right)^{2}}\right)$$
Tercera derivada
[src]
/ 3 / 2 \ 3 2 \
cot(3*x) |/ / 6\ \ 2 / / 6\ \ | 4 / 6\ / 2 \ / 6\| 4 / 2 \ 3 3 / 6\ / 6\ / 6\ / 2 \ / 2 \ / 6\ |
/ / 6\\ || / 2 \ / / 6\\ \1 + 7*x /*cot(3*x)| / 2 \ / / 6\\ | / 2 \ / / 6\\ \1 + 7*x /*cot(3*x)| | / 2 \ / / 6\\ 42*x *cot(3*x) \1 + 7*x / *cot(3*x) 6*\1 + cot (3*x)/*\1 + 7*x /| 378*x *\1 + cot (3*x)/ 2 / 2 \ / / 6\\ 210*x *cot(3*x) 126*x *\1 + 7*x /*cot(3*x) 2*\1 + 7*x / *cot(3*x) 9*\1 + 7*x / *\1 + cot (3*x)/ 54*\1 + cot (3*x)/*\1 + 7*x /*cot(3*x)|
\x*\1 + x // *||- 3*\1 + cot (3*x)/*log\x*\1 + x // + -------------------| - 54*\1 + cot (3*x)/ *log\x*\1 + x // + 3*|- 3*\1 + cot (3*x)/*log\x*\1 + x // + -------------------|*|18*\1 + cot (3*x)/*cot(3*x)*log\x*\1 + x // + -------------- - -------------------- - ----------------------------| - ---------------------- - 108*cot (3*x)*\1 + cot (3*x)/*log\x*\1 + x // + --------------- - -------------------------- + ---------------------- + ----------------------------- + --------------------------------------|
|| / 6\ | | / 6\ | | 6 2 / 6\ | 6 6 2 3 2 / 6\ |
|\ x*\1 + x / / \ x*\1 + x / / | 1 + x 2 / 6\ x*\1 + x / | 1 + x 1 + x / 6\ 3 / 6\ 2 / 6\ x*\1 + x / |
\ \ x *\1 + x / / \1 + x / x *\1 + x / x *\1 + x / /
$$\left(x \left(x^{6} + 1\right)\right)^{\cot{\left(3 x \right)}} \left(- \frac{378 x^{4} \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x^{6} + 1} + \frac{210 x^{3} \cot{\left(3 x \right)}}{x^{6} + 1} - \frac{126 x^{3} \left(7 x^{6} + 1\right) \cot{\left(3 x \right)}}{\left(x^{6} + 1\right)^{2}} + \left(- 3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(x \left(x^{6} + 1\right) \right)} + \frac{\left(7 x^{6} + 1\right) \cot{\left(3 x \right)}}{x \left(x^{6} + 1\right)}\right)^{3} + 3 \left(- 3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(x \left(x^{6} + 1\right) \right)} + \frac{\left(7 x^{6} + 1\right) \cot{\left(3 x \right)}}{x \left(x^{6} + 1\right)}\right) \left(\frac{42 x^{4} \cot{\left(3 x \right)}}{x^{6} + 1} + 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(x \left(x^{6} + 1\right) \right)} \cot{\left(3 x \right)} - \frac{6 \left(7 x^{6} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x \left(x^{6} + 1\right)} - \frac{\left(7 x^{6} + 1\right)^{2} \cot{\left(3 x \right)}}{x^{2} \left(x^{6} + 1\right)^{2}}\right) - 54 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(x \left(x^{6} + 1\right) \right)} - 108 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(x \left(x^{6} + 1\right) \right)} \cot^{2}{\left(3 x \right)} + \frac{54 \left(7 x^{6} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)}}{x \left(x^{6} + 1\right)} + \frac{9 \left(7 x^{6} + 1\right)^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x^{2} \left(x^{6} + 1\right)^{2}} + \frac{2 \left(7 x^{6} + 1\right)^{3} \cot{\left(3 x \right)}}{x^{3} \left(x^{6} + 1\right)^{3}}\right)$$