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*cos(3*x)
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Derivada de x^(7/6)
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Expresiones idénticas
- y=(x^ seis +7x)^(ctgx)
- y es igual a (x en el grado 6 más 7x) en el grado (ctgx)
- y es igual a (x en el grado seis más 7x) en el grado (ctgx)
- y=(x6+7x)(ctgx)
- y=x6+7xctgx
- y=(x⁶+7x)^(ctgx)
- y=x^6+7x^ctgx
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Expresiones semejantes
- y=(x^6-7x)^(ctgx)
Derivada de y=(x^6+7x)^(ctgx)
Solución
Ha introducido
[src]
cot(x) / 6 \ \x + 7*x/
$$\left(x^{6} + 7 x\right)^{\cot{\left(x \right)}}$$
(x^6 + 7*x)^cot(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(x) / / 5\ \
/ 6 \ |/ 2 \ / 6 \ \7 + 6*x /*cot(x)|
\x + 7*x/ *|\-1 - cot (x)/*log\x + 7*x/ + -----------------|
| 6 |
\ x + 7*x /
$$\left(x^{6} + 7 x\right)^{\cot{\left(x \right)}} \left(\frac{\left(6 x^{5} + 7\right) \cot{\left(x \right)}}{x^{6} + 7 x} + \left(- \cot^{2}{\left(x \right)} - 1\right) \log{\left(x^{6} + 7 x \right)}\right)$$
Segunda derivada
[src]
/ 2 2 \
cot(x) |/ / 5\ \ 3 / 5\ / 2 \ / 5\|
/ / 5\\ || / 2 \ / / 5\\ \7 + 6*x /*cot(x)| / 2 \ / / 5\\ 30*x *cot(x) \7 + 6*x / *cot(x) 2*\1 + cot (x)/*\7 + 6*x /|
\x*\7 + x // *||- \1 + cot (x)/*log\x*\7 + x // + -----------------| + 2*\1 + cot (x)/*cot(x)*log\x*\7 + x // + ------------ - ------------------ - --------------------------|
|| / 5\ | 5 2 / 5\ |
|\ x*\7 + x / / 7 + x 2 / 5\ x*\7 + x / |
\ x *\7 + x / /
$$\left(x \left(x^{5} + 7\right)\right)^{\cot{\left(x \right)}} \left(\frac{30 x^{3} \cot{\left(x \right)}}{x^{5} + 7} + \left(- \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \left(x^{5} + 7\right) \right)} + \frac{\left(6 x^{5} + 7\right) \cot{\left(x \right)}}{x \left(x^{5} + 7\right)}\right)^{2} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \left(x^{5} + 7\right) \right)} \cot{\left(x \right)} - \frac{2 \left(6 x^{5} + 7\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{x \left(x^{5} + 7\right)} - \frac{\left(6 x^{5} + 7\right)^{2} \cot{\left(x \right)}}{x^{2} \left(x^{5} + 7\right)^{2}}\right)$$
Tercera derivada
[src]
/ 3 / 2 \ 3 2 \
cot(x) |/ / 5\ \ 2 / / 5\ \ | 3 / 5\ / 2 \ / 5\| 3 / 2 \ 2 2 / 5\ / 5\ / 5\ / 2 \ / 2 \ / 5\ |
/ / 5\\ || / 2 \ / / 5\\ \7 + 6*x /*cot(x)| / 2 \ / / 5\\ | / 2 \ / / 5\\ \7 + 6*x /*cot(x)| | / 2 \ / / 5\\ 30*x *cot(x) \7 + 6*x / *cot(x) 2*\1 + cot (x)/*\7 + 6*x /| 90*x *\1 + cot (x)/ 2 / 2 \ / / 5\\ 120*x *cot(x) 90*x *\7 + 6*x /*cot(x) 2*\7 + 6*x / *cot(x) 3*\7 + 6*x / *\1 + cot (x)/ 6*\1 + cot (x)/*\7 + 6*x /*cot(x)|
\x*\7 + x // *||- \1 + cot (x)/*log\x*\7 + x // + -----------------| - 2*\1 + cot (x)/ *log\x*\7 + x // + 3*|- \1 + cot (x)/*log\x*\7 + x // + -----------------|*|2*\1 + cot (x)/*cot(x)*log\x*\7 + x // + ------------ - ------------------ - --------------------------| - ------------------- - 4*cot (x)*\1 + cot (x)/*log\x*\7 + x // + ------------- - ----------------------- + -------------------- + --------------------------- + ---------------------------------|
|| / 5\ | | / 5\ | | 5 2 / 5\ | 5 5 2 3 2 / 5\ |
|\ x*\7 + x / / \ x*\7 + x / / | 7 + x 2 / 5\ x*\7 + x / | 7 + x 7 + x / 5\ 3 / 5\ 2 / 5\ x*\7 + x / |
\ \ x *\7 + x / / \7 + x / x *\7 + x / x *\7 + x / /
$$\left(x \left(x^{5} + 7\right)\right)^{\cot{\left(x \right)}} \left(- \frac{90 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{5} + 7} + \frac{120 x^{2} \cot{\left(x \right)}}{x^{5} + 7} - \frac{90 x^{2} \left(6 x^{5} + 7\right) \cot{\left(x \right)}}{\left(x^{5} + 7\right)^{2}} + \left(- \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \left(x^{5} + 7\right) \right)} + \frac{\left(6 x^{5} + 7\right) \cot{\left(x \right)}}{x \left(x^{5} + 7\right)}\right)^{3} + 3 \left(- \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \left(x^{5} + 7\right) \right)} + \frac{\left(6 x^{5} + 7\right) \cot{\left(x \right)}}{x \left(x^{5} + 7\right)}\right) \left(\frac{30 x^{3} \cot{\left(x \right)}}{x^{5} + 7} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \left(x^{5} + 7\right) \right)} \cot{\left(x \right)} - \frac{2 \left(6 x^{5} + 7\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{x \left(x^{5} + 7\right)} - \frac{\left(6 x^{5} + 7\right)^{2} \cot{\left(x \right)}}{x^{2} \left(x^{5} + 7\right)^{2}}\right) - 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \left(x^{5} + 7\right) \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \left(x^{5} + 7\right) \right)} \cot^{2}{\left(x \right)} + \frac{6 \left(6 x^{5} + 7\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x \left(x^{5} + 7\right)} + \frac{3 \left(6 x^{5} + 7\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{2} \left(x^{5} + 7\right)^{2}} + \frac{2 \left(6 x^{5} + 7\right)^{3} \cot{\left(x \right)}}{x^{3} \left(x^{5} + 7\right)^{3}}\right)$$
Gráfico