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 (3x^4-x)^7
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Derivada de (3x+6)^2
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Derivada de (1+cos(x))/(1-cos(x))
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Derivada de (2*x-9)/(x-5)
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Expresiones idénticas
- y=(x^ tres - uno)^tg2x
- y es igual a (x al cubo menos 1) en el grado tg2x
- y es igual a (x en el grado tres menos uno) en el grado tg2x
- y=(x3-1)tg2x
- y=x3-1tg2x
- y=(x³-1)^tg2x
- y=(x en el grado 3-1) en el grado tg2x
- y=x^3-1^tg2x
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Expresiones semejantes
- y=(x^3+1)^tg2x
Derivada de y=(x^3-1)^tg2x
Solución
Ha introducido
[src]
tan(2*x) / 3 \ \x - 1/
$$\left(x^{3} - 1\right)^{\tan{\left(2 x \right)}}$$
(x^3 - 1)^tan(2*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
tan(2*x) / 2 \
/ 3 \ |/ 2 \ / 3 \ 3*x *tan(2*x)|
\x - 1/ *|\2 + 2*tan (2*x)/*log\x - 1/ + -------------|
| 3 |
\ x - 1 /
$$\left(x^{3} - 1\right)^{\tan{\left(2 x \right)}} \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + \left(2 \tan^{2}{\left(2 x \right)} + 2\right) \log{\left(x^{3} - 1 \right)}\right)$$
Segunda derivada
[src]
/ 2 \
tan(2*x) |/ 2 \ 4 2 / 2 \|
/ 3\ || / 2 \ / 3\ 3*x *tan(2*x)| 9*x *tan(2*x) 6*x*tan(2*x) / 2 \ / 3\ 12*x *\1 + tan (2*x)/|
\-1 + x / *||2*\1 + tan (2*x)/*log\-1 + x / + -------------| - ------------- + ------------ + 8*\1 + tan (2*x)/*log\-1 + x /*tan(2*x) + ---------------------|
|| 3 | 2 3 3 |
|\ -1 + x / / 3\ -1 + x -1 + x |
\ \-1 + x / /
$$\left(x^{3} - 1\right)^{\tan{\left(2 x \right)}} \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} - 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} - 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)}\right)^{2} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)} \tan{\left(2 x \right)}\right)$$
3-я производная
[src]
/ 3 \
tan(2*x) |/ 2 \ / 2 \ / 4 2 / 2 \\ 2 3 4 / 2 \ / 2 \ 6 2 / 2 \ |
/ 3\ || / 2 \ / 3\ 3*x *tan(2*x)| | / 2 \ / 3\ 3*x *tan(2*x)| | 9*x *tan(2*x) 6*x*tan(2*x) / 2 \ / 3\ 12*x *\1 + tan (2*x)/| 6*tan(2*x) / 2 \ / 3\ 54*x *tan(2*x) 54*x *\1 + tan (2*x)/ 2 / 2 \ / 3\ 36*x*\1 + tan (2*x)/ 54*x *tan(2*x) 72*x *\1 + tan (2*x)/*tan(2*x)|
\-1 + x / *||2*\1 + tan (2*x)/*log\-1 + x / + -------------| + 3*|2*\1 + tan (2*x)/*log\-1 + x / + -------------|*|- ------------- + ------------ + 8*\1 + tan (2*x)/*log\-1 + x /*tan(2*x) + ---------------------| + ---------- + 16*\1 + tan (2*x)/ *log\-1 + x / - -------------- - --------------------- + 32*tan (2*x)*\1 + tan (2*x)/*log\-1 + x / + -------------------- + -------------- + ------------------------------|
|| 3 | | 3 | | 2 3 3 | 3 2 2 3 3 3 |
|\ -1 + x / \ -1 + x / | / 3\ -1 + x -1 + x | -1 + x / 3\ / 3\ -1 + x / 3\ -1 + x |
\ \ \-1 + x / / \-1 + x / \-1 + x / \-1 + x / /
$$\left(x^{3} - 1\right)^{\tan{\left(2 x \right)}} \left(\frac{54 x^{6} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{3}} - \frac{54 x^{4} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\left(x^{3} - 1\right)^{2}} - \frac{54 x^{3} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{2}} + \frac{72 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)}}{x^{3} - 1} + \frac{36 x \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} - 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)}\right)^{3} + 3 \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)}\right) \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} - 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} - 1} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)} \tan{\left(2 x \right)}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x^{3} - 1 \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)} \tan^{2}{\left(2 x \right)} + \frac{6 \tan{\left(2 x \right)}}{x^{3} - 1}\right)$$
Tercera derivada
[src]
/ 3 \
tan(2*x) |/ 2 \ / 2 \ / 4 2 / 2 \\ 2 3 4 / 2 \ / 2 \ 6 2 / 2 \ |
/ 3\ || / 2 \ / 3\ 3*x *tan(2*x)| | / 2 \ / 3\ 3*x *tan(2*x)| | 9*x *tan(2*x) 6*x*tan(2*x) / 2 \ / 3\ 12*x *\1 + tan (2*x)/| 6*tan(2*x) / 2 \ / 3\ 54*x *tan(2*x) 54*x *\1 + tan (2*x)/ 2 / 2 \ / 3\ 36*x*\1 + tan (2*x)/ 54*x *tan(2*x) 72*x *\1 + tan (2*x)/*tan(2*x)|
\-1 + x / *||2*\1 + tan (2*x)/*log\-1 + x / + -------------| + 3*|2*\1 + tan (2*x)/*log\-1 + x / + -------------|*|- ------------- + ------------ + 8*\1 + tan (2*x)/*log\-1 + x /*tan(2*x) + ---------------------| + ---------- + 16*\1 + tan (2*x)/ *log\-1 + x / - -------------- - --------------------- + 32*tan (2*x)*\1 + tan (2*x)/*log\-1 + x / + -------------------- + -------------- + ------------------------------|
|| 3 | | 3 | | 2 3 3 | 3 2 2 3 3 3 |
|\ -1 + x / \ -1 + x / | / 3\ -1 + x -1 + x | -1 + x / 3\ / 3\ -1 + x / 3\ -1 + x |
\ \ \-1 + x / / \-1 + x / \-1 + x / \-1 + x / /
$$\left(x^{3} - 1\right)^{\tan{\left(2 x \right)}} \left(\frac{54 x^{6} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{3}} - \frac{54 x^{4} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{\left(x^{3} - 1\right)^{2}} - \frac{54 x^{3} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{2}} + \frac{72 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)}}{x^{3} - 1} + \frac{36 x \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} - 1} + \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)}\right)^{3} + 3 \left(\frac{3 x^{2} \tan{\left(2 x \right)}}{x^{3} - 1} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)}\right) \left(- \frac{9 x^{4} \tan{\left(2 x \right)}}{\left(x^{3} - 1\right)^{2}} + \frac{12 x^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{3} - 1} + \frac{6 x \tan{\left(2 x \right)}}{x^{3} - 1} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)} \tan{\left(2 x \right)}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x^{3} - 1 \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x^{3} - 1 \right)} \tan^{2}{\left(2 x \right)} + \frac{6 \tan{\left(2 x \right)}}{x^{3} - 1}\right)$$
Gráfico