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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+3)
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Derivada de 4*y
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Derivada de (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- y=((x^ ocho + uno)^thx)
- y es igual a ((x en el grado 8 más 1) en el grado thx)
- y es igual a ((x en el grado ocho más uno) en el grado thx)
- y=((x8+1)thx)
- y=x8+1thx
- y=((x⁸+1)^thx)
- y=x^8+1^thx
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Expresiones semejantes
- y=((x^8-1)^thx)
Derivada de y=((x^8+1)^thx)
Solución
Ha introducido
[src]
tanh(x) / 8 \ \x + 1/
$$\left(x^{8} + 1\right)^{\tanh{\left(x \right)}}$$
(x^8 + 1)^tanh(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
tanh(x) / 7 \
/ 8 \ |/ 2 \ / 8 \ 8*x *tanh(x)|
\x + 1/ *|\1 - tanh (x)/*log\x + 1/ + ------------|
| 8 |
\ x + 1 /
$$\left(x^{8} + 1\right)^{\tanh{\left(x \right)}} \left(\frac{8 x^{7} \tanh{\left(x \right)}}{x^{8} + 1} + \left(1 - \tanh^{2}{\left(x \right)}\right) \log{\left(x^{8} + 1 \right)}\right)$$
Segunda derivada
[src]
/ 2 \
tanh(x) |/ 7 \ 14 7 / 2 \ 6 |
/ 8\ || / 2 \ / 8\ 8*x *tanh(x)| 64*x *tanh(x) 16*x *\-1 + tanh (x)/ / 2 \ / 8\ 56*x *tanh(x)|
\1 + x / *||- \-1 + tanh (x)/*log\1 + x / + ------------| - -------------- - --------------------- + 2*\-1 + tanh (x)/*log\1 + x /*tanh(x) + -------------|
|| 8 | 2 8 8 |
|\ 1 + x / / 8\ 1 + x 1 + x |
\ \1 + x / /
$$\left(x^{8} + 1\right)^{\tanh{\left(x \right)}} \left(- \frac{64 x^{14} \tanh{\left(x \right)}}{\left(x^{8} + 1\right)^{2}} - \frac{16 x^{7} \left(\tanh^{2}{\left(x \right)} - 1\right)}{x^{8} + 1} + \frac{56 x^{6} \tanh{\left(x \right)}}{x^{8} + 1} + \left(\frac{8 x^{7} \tanh{\left(x \right)}}{x^{8} + 1} - \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x^{8} + 1 \right)}\right)^{2} + 2 \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x^{8} + 1 \right)} \tanh{\left(x \right)}\right)$$
Tercera derivada
[src]
/ 3 \
tanh(x) |/ 7 \ / 7 \ / 6 7 / 2 \ 14 \ 2 13 6 / 2 \ 14 / 2 \ 5 21 7 / 2 \ |
/ 8\ || / 2 \ / 8\ 8*x *tanh(x)| | / 2 \ / 8\ 8*x *tanh(x)| | / 2 \ / 8\ 28*x *tanh(x) 8*x *\-1 + tanh (x)/ 32*x *tanh(x)| / 2 \ / 8\ 1344*x *tanh(x) 168*x *\-1 + tanh (x)/ 2 / 2 \ / 8\ 192*x *\-1 + tanh (x)/ 336*x *tanh(x) 1024*x *tanh(x) 48*x *\-1 + tanh (x)/*tanh(x)|
\1 + x / *||- \-1 + tanh (x)/*log\1 + x / + ------------| - 6*|- \-1 + tanh (x)/*log\1 + x / + ------------|*|- \-1 + tanh (x)/*log\1 + x /*tanh(x) - ------------- + -------------------- + --------------| - 2*\-1 + tanh (x)/ *log\1 + x / - ---------------- - ---------------------- - 4*tanh (x)*\-1 + tanh (x)/*log\1 + x / + ----------------------- + -------------- + ---------------- + -----------------------------|
|| 8 | | 8 | | 8 8 2 | 2 8 2 8 3 8 |
|\ 1 + x / \ 1 + x / | 1 + x 1 + x / 8\ | / 8\ 1 + x / 8\ 1 + x / 8\ 1 + x |
\ \ \1 + x / / \1 + x / \1 + x / \1 + x / /
$$\left(x^{8} + 1\right)^{\tanh{\left(x \right)}} \left(\frac{1024 x^{21} \tanh{\left(x \right)}}{\left(x^{8} + 1\right)^{3}} + \frac{192 x^{14} \left(\tanh^{2}{\left(x \right)} - 1\right)}{\left(x^{8} + 1\right)^{2}} - \frac{1344 x^{13} \tanh{\left(x \right)}}{\left(x^{8} + 1\right)^{2}} + \frac{48 x^{7} \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)}}{x^{8} + 1} - \frac{168 x^{6} \left(\tanh^{2}{\left(x \right)} - 1\right)}{x^{8} + 1} + \frac{336 x^{5} \tanh{\left(x \right)}}{x^{8} + 1} + \left(\frac{8 x^{7} \tanh{\left(x \right)}}{x^{8} + 1} - \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x^{8} + 1 \right)}\right)^{3} - 6 \left(\frac{8 x^{7} \tanh{\left(x \right)}}{x^{8} + 1} - \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x^{8} + 1 \right)}\right) \left(\frac{32 x^{14} \tanh{\left(x \right)}}{\left(x^{8} + 1\right)^{2}} + \frac{8 x^{7} \left(\tanh^{2}{\left(x \right)} - 1\right)}{x^{8} + 1} - \frac{28 x^{6} \tanh{\left(x \right)}}{x^{8} + 1} - \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x^{8} + 1 \right)} \tanh{\left(x \right)}\right) - 2 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} \log{\left(x^{8} + 1 \right)} - 4 \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x^{8} + 1 \right)} \tanh^{2}{\left(x \right)}\right)$$
Gráfico