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 -2*y
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Derivada de 3^2*x
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Derivada de 2*x+8/x
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Derivada de -1/y
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Expresiones idénticas
- y=(4x^ tres -6x)^ctg3x
- y es igual a (4x al cubo menos 6x) en el grado ctg3x
- y es igual a (4x en el grado tres menos 6x) en el grado ctg3x
- y=(4x3-6x)ctg3x
- y=4x3-6xctg3x
- y=(4x³-6x)^ctg3x
- y=(4x en el grado 3-6x) en el grado ctg3x
- y=4x^3-6x^ctg3x
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Expresiones semejantes
- y=(4x^3+6x)^ctg3x
Derivada de y=(4x^3-6x)^ctg3x
Solución
Ha introducido
[src]
cot(3*x) / 3 \ \4*x - 6*x/
$$\left(4 x^{3} - 6 x\right)^{\cot{\left(3 x \right)}}$$
(4*x^3 - 6*x)^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) / / 2\ \
/ 3 \ |/ 2 \ / 3 \ \-6 + 12*x /*cot(3*x)|
\4*x - 6*x/ *|\-3 - 3*cot (3*x)/*log\4*x - 6*x/ + ---------------------|
| 3 |
\ 4*x - 6*x /
$$\left(4 x^{3} - 6 x\right)^{\cot{\left(3 x \right)}} \left(\frac{\left(12 x^{2} - 6\right) \cot{\left(3 x \right)}}{4 x^{3} - 6 x} + \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) \log{\left(4 x^{3} - 6 x \right)}\right)$$
Segunda derivada
[src]
/ 2 2 \
cot(3*x) | / / 2\ \ / 2 \ / 2\ / 2\ |
/ / 2\\ | | / 2 \ / / 2\\ \-1 + 2*x /*cot(3*x)| 4*cot(3*x) / 2 \ / / 2\\ 6*\1 + cot (3*x)/*\-1 + 2*x / 3*\-1 + 2*x / *cot(3*x)|
3*\2*x*\-3 + 2*x // *|3*|- \1 + cot (3*x)/*log\2*x*\-3 + 2*x // + --------------------| + ---------- + 6*\1 + cot (3*x)/*cot(3*x)*log\2*x*\-3 + 2*x // - ----------------------------- - -----------------------|
| | / 2\ | 2 / 2\ 2 |
| \ x*\-3 + 2*x / / -3 + 2*x x*\-3 + 2*x / 2 / 2\ |
\ x *\-3 + 2*x / /
$$3 \left(2 x \left(2 x^{2} - 3\right)\right)^{\cot{\left(3 x \right)}} \left(3 \left(- \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} + \frac{\left(2 x^{2} - 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)}\right)^{2} + 6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} \cot{\left(3 x \right)} + \frac{4 \cot{\left(3 x \right)}}{2 x^{2} - 3} - \frac{6 \left(2 x^{2} - 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x \left(2 x^{2} - 3\right)} - \frac{3 \left(2 x^{2} - 1\right)^{2} \cot{\left(3 x \right)}}{x^{2} \left(2 x^{2} - 3\right)^{2}}\right)$$
Tercera derivada
[src]
/ 3 / 2 \ 3 2 \
cot(3*x) | / / 2\ \ / 2 \ 2 / / 2\ \ | / 2 \ / 2\ / 2\ | / 2\ / 2\ / 2\ / 2 \ / 2 \ / 2\ |
/ / 2\\ | | / 2 \ / / 2\\ \-1 + 2*x /*cot(3*x)| 36*\1 + cot (3*x)/ / 2 \ / / 2\\ | / 2 \ / / 2\\ \-1 + 2*x /*cot(3*x)| |4*cot(3*x) / 2 \ / / 2\\ 6*\1 + cot (3*x)/*\-1 + 2*x / 3*\-1 + 2*x / *cot(3*x)| 2 / 2 \ / / 2\\ 4*cot(3*x) 36*\-1 + 2*x /*cot(3*x) 18*\-1 + 2*x / *cot(3*x) 27*\-1 + 2*x / *\1 + cot (3*x)/ 54*\1 + cot (3*x)/*\-1 + 2*x /*cot(3*x)|
3*\2*x*\-3 + 2*x // *|9*|- \1 + cot (3*x)/*log\2*x*\-3 + 2*x // + --------------------| - ------------------ - 18*\1 + cot (3*x)/ *log\2*x*\-3 + 2*x // + 9*|- \1 + cot (3*x)/*log\2*x*\-3 + 2*x // + --------------------|*|---------- + 6*\1 + cot (3*x)/*cot(3*x)*log\2*x*\-3 + 2*x // - ----------------------------- - -----------------------| - 36*cot (3*x)*\1 + cot (3*x)/*log\2*x*\-3 + 2*x // + ------------- - ----------------------- + ------------------------ + ------------------------------- + ---------------------------------------|
| | / 2\ | 2 | / 2\ | | 2 / 2\ 2 | / 2\ 2 3 2 / 2\ |
| \ x*\-3 + 2*x / / -3 + 2*x \ x*\-3 + 2*x / / |-3 + 2*x x*\-3 + 2*x / 2 / 2\ | x*\-3 + 2*x / / 2\ 3 / 2\ 2 / 2\ x*\-3 + 2*x / |
\ \ x *\-3 + 2*x / / x*\-3 + 2*x / x *\-3 + 2*x / x *\-3 + 2*x / /
$$3 \left(2 x \left(2 x^{2} - 3\right)\right)^{\cot{\left(3 x \right)}} \left(9 \left(- \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} + \frac{\left(2 x^{2} - 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)}\right)^{3} + 9 \left(- \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} + \frac{\left(2 x^{2} - 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)}\right) \left(6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} \cot{\left(3 x \right)} + \frac{4 \cot{\left(3 x \right)}}{2 x^{2} - 3} - \frac{6 \left(2 x^{2} - 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x \left(2 x^{2} - 3\right)} - \frac{3 \left(2 x^{2} - 1\right)^{2} \cot{\left(3 x \right)}}{x^{2} \left(2 x^{2} - 3\right)^{2}}\right) - 18 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(2 x \left(2 x^{2} - 3\right) \right)} - 36 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} \cot^{2}{\left(3 x \right)} - \frac{36 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{2 x^{2} - 3} + \frac{54 \left(2 x^{2} - 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)} + \frac{4 \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)} - \frac{36 \left(2 x^{2} - 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)^{2}} + \frac{27 \left(2 x^{2} - 1\right)^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x^{2} \left(2 x^{2} - 3\right)^{2}} + \frac{18 \left(2 x^{2} - 1\right)^{3} \cot{\left(3 x \right)}}{x^{3} \left(2 x^{2} - 3\right)^{3}}\right)$$
Gráfico